![](\"resources/question-resources/Component.gif\"/)
Some basic tasks involving vectors, including converting to/from component form, scalar product, resultant vectors.
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\nYou are going to calculate the magnitude and direction of this vector. Refer to the diagram below:
\n
What is the horizontal component of $\\underline{v}$?
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", "minValue": "{y}", "maxValue": "{y}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "Calculate the magnitude of $\\underline{v}$.
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", "minValue": "{angle}", "maxValue": "{angle}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "dp", "precision": 0, "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": true, "showPrecisionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "question"}, {"name": "Calculate component form of vector", "extensions": [], "custom_part_types": [], "resources": ["question-resources/Component.gif"], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Martin Jones", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/145/"}], "tags": [], "metadata": {"description": "", "licence": "None specified"}, "statement": "A ship travels $\\var{m}$ nautical miles on a bearing of $\\var{d}^\\circ$.
\nYou will calculate its horizontal (east/west) component and its vertical (north/south) component.
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\nThe ship has travelled [[0]] and [[1]].
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\nWest and South will give a negative component.
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\nRefer to Lesson 1 for examples.
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\nRefer to Lesson 1 for examples.
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\nCalculate the following vectors:
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\n\\[A=(\\var{x1},\\var{y1},\\var{z1})\\qquad B=(\\var{x2},\\var{y2},\\var{z2})\\qquad C=(\\var{x3},\\var{y3},\\var{z3})\\]
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\nOtherwise the points are not colinear.
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\n$\\overrightarrow{BC}=$ [[0]]$\\times\\overrightarrow{AB}$
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", "advice": "", "rulesets": {}, "variables": {"angle": {"name": "angle", "group": "Ungrouped variables", "definition": "degrees(arccos(sp/(r1*r2)))", "description": "", "templateType": "anything"}, "y2": {"name": "y2", "group": "Ungrouped variables", "definition": "random(-5..5 except 0)", "description": "", "templateType": "anything"}, "x2": {"name": "x2", "group": "Ungrouped variables", "definition": "random(-5..5)", "description": "", "templateType": "anything"}, "sp": {"name": "sp", "group": "Ungrouped variables", "definition": "x1*x2+y1*y2+z1*z2", "description": "", "templateType": "anything"}, "r2": {"name": "r2", "group": "Ungrouped variables", "definition": "sqrt(x2^2+y2^2+z2^2)", "description": "", "templateType": "anything"}, "x1": {"name": "x1", "group": "Ungrouped variables", "definition": "random(-5..5)", "description": "", "templateType": "anything"}, "r1": {"name": "r1", "group": "Ungrouped variables", "definition": "sqrt(x1^2+y1^2+z1^2)", "description": "", "templateType": "anything"}, "y1": {"name": "y1", "group": "Ungrouped variables", "definition": "random(-5..5)", "description": "", "templateType": "anything"}, "z1": {"name": "z1", "group": "Ungrouped variables", "definition": "random(-5..5 except 0)", "description": "", "templateType": "anything"}, "z2": {"name": "z2", "group": "Ungrouped variables", "definition": "random(-5..5 except z1*y2/y1)", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["x1", "y1", "z1", "x2", "y2", "z2", "r1", "r2", "sp", "angle"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "What is $|\\underline{a}|$?
", "stepsPenalty": 0, "steps": [{"type": "information", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "$|\\underline{a}|$ is the magnitude of vector $\\underline{a}$. Refer to Lesson 1.
"}], "minValue": "{r1}", "maxValue": "{r1}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "dp", "precision": "2", "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": true, "showPrecisionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "What is $|\\underline{b}|$?
", "minValue": "{r2}", "maxValue": "{r2}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "dp", "precision": "2", "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": true, "showPrecisionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "Calculate $\\underline{a}\\cdot\\underline{b}$
", "stepsPenalty": 0, "steps": [{"type": "information", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "$\\underline{a}\\cdot\\underline{b}$ is the scalar product of vectors $\\underline{a}$ and $\\underline{b}$. Refer to Lesson 3.
"}], "minValue": "{sp}", "maxValue": "{sp}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "Now calculate the angle between vectors $\\underline{a}$ and $\\underline{b}$.
", "stepsPenalty": 0, "steps": [{"type": "information", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "Rearrange the following formula:
\n\\[\\underline{a}\\cdot\\underline{b}=|\\underline{a}||\\underline{b}|\\cos{\\theta}\\]
\nRefer to Lesson 3 for examples.
"}], "minValue": "{angle}", "maxValue": "{angle}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "precisionType": "dp", "precision": 0, "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": true, "showPrecisionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "question"}, {"name": "Calculate resultant vector", "extensions": ["quantities"], "custom_part_types": [{"source": {"pk": 7, "author": {"name": "Christian Lawson-Perfect", "pk": 7}, "edit_page": "/part_type/7/edit"}, "name": "Quantity with units", "short_name": "quantity", "description": "The student enters a quantity with units.
", "help_url": "https://github.com/numbas/numbas-extension-quantities", "input_widget": "string", "input_options": {"correctAnswer": "plain_string(settings[\"correctAnswer\"])", "hint": {"static": false, "value": "switch(\n settings[\"hint\"]=\"remind units\",\n \"Include units in your answer.\",\n settings[\"hint\"]=\"show units\",\n \"Give your answer in \"+units_string(settings[\"correctAnswer\"])\n ,\n \"\"\n)"}, "allowEmpty": {"static": true, "value": false}}, "can_be_gap": true, "can_be_step": true, "marking_script": "mark:\napply(valid_number);\napply(student_quantity);\napply(has_units);\napply(compatible);\ntry(\n correctif(close_enough),\n x,\n apply(student_quantity)\n);\napply(same_units)\n\ninterpreted_answer:\nstudent_quantity\n\nallowed_notation_styles:\n[\"plain\",\"en\"]\n\nmatch_student_number:\nmatchnumber(studentAnswer,allowed_notation_styles)\n\nstudent_number:\nmatch_student_number[1]\n\nraw_student_units:\ntry(\n quantity(studentAnswer[len(match_student_number[0])..len(studentAnswer)]),\n message,\n warn(\"Your answer is not a valid quantity.\");\n fail(\"Your answer is not a valid quantity.\")\n)\n\nstudent_units:\nif(compatible(raw_student_units,correct_units) or settings[\"incompatible_units_action\"]<>\"convert\",\n raw_student_units,\n correct_units\n)\n\nstudent_quantity:\napply(student_units);\ntry(\n student_number * student_units,\n message,\n warn(\"Your answer is not a valid quantity.\");\n fail(\"Your answer is not a valid quantity.\")\n)\n\ncorrect_quantity:\nsettings[\"correctAnswer\"]\n\ncompatible:\nif(compatible(raw_student_units,correct_quantity),\n true\n,\n let(message,\"Your answer does not have the correct dimensions.\",\n if(settings[\"incompatible_units_action\"]=\"prevent\",\n warn(message);\n fail(message)\n ,\n if(settings[\"incompatible_units_action\"]=\"convert\",\n incorrect(\"Your answer does not have the correct dimensions. It will be marked as if the correct dimensions were used, and then a penalty will be applied.\")\n ,\n incorrect(\"Your answer does not have the correct dimensions.\");\n end()\n )\n );\n false\n )\n)\n\ncorrect_units:\nunits(correct_quantity)\n\nsame_units:\nassert(raw_student_units=correct_units,\n let(\n message,if(settings[\"hint\"]=\"show units\",\"You did not give your answer in \"+units_string(correct_units)+\".\", \"Your answer is not in the expected units.\"),\n switch(\n settings[\"different_units_action\"]=\"prevent\",\n warn(message);\n fail(message)\n ,\n settings[\"different_units_action\"]=\"incorrect\",\n incorrect(message); \n warn(message);\n end()\n ,\n settings[\"different_units_action\"]=\"warn\",\n warn(message);\n multiply_credit(1-settings[\"different_units_penalty\"],message)\n ,\n settings[\"different_units_penalty\"]<1,\n multiply_credit(1-settings[\"different_units_penalty\"],message)\n ,\n false\n )\n );\n false\n)\n\nhas_units:\nassert(not unitless(student_quantity),\n assert(settings[\"allow_unitless\"],\n warn(\"You must include the units in your answer.\");\n fail(\"You did not include units in your answer.\")\n )\n)\n\ncan_compare:\ncompatible or settings[\"incompatible_units_action\"]=\"convert\"\n\nclose_enough:\nif(can_compare,\n student_quantity>=correct_quantity - wiggle \n and \n student_quantity<=correct_quantity + wiggle \n,\n false\n)\n\nwiggle:\nunits(correct_quantity)*abs(eval(settings[\"wiggle\"]))\n\nvalid_number:\nif(isNaN(student_number),\n warn(translate(\"part.numberentry.answer invalid\"));\n fail(translate(\"part.numberentry.answer invalid\"))\n,\n true\n )", "marking_notes": [{"name": "mark", "description": "This is the main marking note. It should award credit and provide feedback based on the student's answer.", "definition": "apply(valid_number);\napply(student_quantity);\napply(has_units);\napply(compatible);\ntry(\n correctif(close_enough),\n x,\n apply(student_quantity)\n);\napply(same_units)"}, {"name": "interpreted_answer", "description": "A value representing the student's answer to this part.", "definition": "student_quantity"}, {"name": "allowed_notation_styles", "description": "", "definition": "[\"plain\",\"en\"]"}, {"name": "match_student_number", "description": "", "definition": "matchnumber(studentAnswer,allowed_notation_styles)"}, {"name": "student_number", "description": "The scalar part of the student's quantity
", "definition": "match_student_number[1]"}, {"name": "raw_student_units", "description": "The units of the student's quantity, before converting.
", "definition": "try(\n quantity(studentAnswer[len(match_student_number[0])..len(studentAnswer)]),\n message,\n warn(\"Your answer is not a valid quantity.\");\n fail(\"Your answer is not a valid quantity.\")\n)"}, {"name": "student_units", "description": "The units of the student's quantity.
\nIf the student used units incompatible with the units in the expected answer, and the \"what to do if incompatible units used\" option is set to \"mark as if correct units used\", the student's units are ignored and the expected units are used instead.
", "definition": "if(compatible(raw_student_units,correct_units) or settings[\"incompatible_units_action\"]<>\"convert\",\n raw_student_units,\n correct_units\n)"}, {"name": "student_quantity", "description": "The student's answer, interpreted as a quantity.
\nMarking fails if the student does not enter a valid quantity.
", "definition": "apply(student_units);\ntry(\n student_number * student_units,\n message,\n warn(\"Your answer is not a valid quantity.\");\n fail(\"Your answer is not a valid quantity.\")\n)"}, {"name": "correct_quantity", "description": "", "definition": "settings[\"correctAnswer\"]"}, {"name": "compatible", "description": "Are the units of the student's quantity compatible with the units of the expected quantity?
", "definition": "if(compatible(raw_student_units,correct_quantity),\n true\n,\n let(message,\"Your answer does not have the correct dimensions.\",\n if(settings[\"incompatible_units_action\"]=\"prevent\",\n warn(message);\n fail(message)\n ,\n if(settings[\"incompatible_units_action\"]=\"convert\",\n incorrect(\"Your answer does not have the correct dimensions. It will be marked as if the correct dimensions were used, and then a penalty will be applied.\")\n ,\n incorrect(\"Your answer does not have the correct dimensions.\");\n end()\n )\n );\n false\n )\n)"}, {"name": "correct_units", "description": "", "definition": "units(correct_quantity)"}, {"name": "same_units", "description": "/Are the student's quantity and the expected quantity in exactly the same units?
", "definition": "assert(raw_student_units=correct_units,\n let(\n message,if(settings[\"hint\"]=\"show units\",\"You did not give your answer in \"+units_string(correct_units)+\".\", \"Your answer is not in the expected units.\"),\n switch(\n settings[\"different_units_action\"]=\"prevent\",\n warn(message);\n fail(message)\n ,\n settings[\"different_units_action\"]=\"incorrect\",\n incorrect(message); \n warn(message);\n end()\n ,\n settings[\"different_units_action\"]=\"warn\",\n warn(message);\n multiply_credit(1-settings[\"different_units_penalty\"],message)\n ,\n settings[\"different_units_penalty\"]<1,\n multiply_credit(1-settings[\"different_units_penalty\"],message)\n ,\n false\n )\n );\n false\n)"}, {"name": "has_units", "description": "", "definition": "assert(not unitless(student_quantity),\n assert(settings[\"allow_unitless\"],\n warn(\"You must include the units in your answer.\");\n fail(\"You did not include units in your answer.\")\n )\n)"}, {"name": "can_compare", "description": "Can the student's answer be compared with the correct answer? True if compatible units used, or \"mark as if correct units used\" selected.
", "definition": "compatible or settings[\"incompatible_units_action\"]=\"convert\""}, {"name": "close_enough", "description": "Is the student's quantity within the allowed tolerance of the expected answer?
", "definition": "if(can_compare,\n student_quantity>=correct_quantity - wiggle \n and \n student_quantity<=correct_quantity + wiggle \n,\n false\n)"}, {"name": "wiggle", "description": "", "definition": "units(correct_quantity)*abs(eval(settings[\"wiggle\"]))"}, {"name": "valid_number", "description": "Is the scalar part of the student's answer a valid number?
", "definition": "if(isNaN(student_number),\n warn(translate(\"part.numberentry.answer invalid\"));\n fail(translate(\"part.numberentry.answer invalid\"))\n,\n true\n )\n"}], "settings": [{"name": "correctAnswer", "label": "Correct answer", "help_url": "", "hint": "The expected quantity.", "input_type": "code", "default_value": "", "evaluate": true}, {"name": "hint", "label": "Input hint", "help_url": "", "hint": "", "input_type": "dropdown", "default_value": "remind units", "choices": [{"value": "none", "label": "None"}, {"value": "remind units", "label": "Remind to include units"}, {"value": "show units", "label": "Show required units"}]}, {"name": "allow_unitless", "label": "Allow unitless answer?", "help_url": "", "hint": "If not ticked, the student is prevented from submitting an answer without specifying units.", "input_type": "checkbox", "default_value": true}, {"name": "incompatible_units_action", "label": "What to do if incompatible units used", "help_url": "", "hint": "If the student's answer is given in units incompatible with the correct answer's units:A body is subject to two forces:
\nWe will calculate the resultant force $F_r$.
\n", "advice": "$F_1$ is purely horizontal so
\n\\[F_1=\\var{mat1}\\]
\nThe horizontal component of $F_2$ is calculated with trigonometry:
\n\\[\\var{m2}\\times\\cos(\\var{d2})=\\var{precround(x2,1)}\\]
\nThe vertical component of $F_2$ is calculated with trigonometry:
\n\\[\\var{m2}\\times\\sin(\\var{d2})=\\var{precround(y2,1)}\\]
\nTherefore, in component form:
\n\\[F_2=\\var{precround(mat2,1)}\\]
\nThe resultant vector $F_r$ is found by adding the vectors $F_1$ and $F_2$.
\n\\[F_r=\\var{mat1}+\\var{precround(mat2,1)}=\\var{precround(mat1+mat2,1)}\\]
\nThe magnitude of the resultant force $F_r$ is calculated with Pythagoras:
\n\\[\\sqrt{\\var{precround(x1+x2,1)}^2+\\var{precround(y2,1)}^2}=\\var{precround(mr,0)}\\]
\nThe direction of the resultant force $F_r$ is calculated with trigonometry:
\n\\[\\tan^{-1}\\left(\\frac{\\var{precround(y2,1)}}{\\var{precround(x1+x2,1)}}\\right)=\\var{precround(dr,0)}^\\circ\\]
\nThe resultant force is acting at {precround(dr,0)}º to the horizontal.
", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {"mat1": {"name": "mat1", "group": "Ungrouped variables", "definition": "matrix([{x1}],[0])", "description": "", "templateType": "anything", "can_override": false}, "mr": {"name": "mr", "group": "Ungrouped variables", "definition": "sqrt((x1+x2)^2+y2^2)", "description": "", "templateType": "anything", "can_override": false}, "mat2": {"name": "mat2", "group": "Ungrouped variables", "definition": "matrix([{x2}],[{y2}])", "description": "", "templateType": "anything", "can_override": false}, "x2": {"name": "x2", "group": "Ungrouped variables", "definition": "m2*cos(radians(d2))", "description": "", "templateType": "anything", "can_override": false}, "y2": {"name": "y2", "group": "Ungrouped variables", "definition": "m2*sin(radians(d2))", "description": "", "templateType": "anything", "can_override": false}, "m2": {"name": "m2", "group": "Ungrouped variables", "definition": "random(10..300 #10)", "description": "", "templateType": "anything", "can_override": false}, "dr": {"name": "dr", "group": "Ungrouped variables", "definition": "degrees(arctan(y2/(x1+x2)))", "description": "", "templateType": "anything", "can_override": false}, "d2": {"name": "d2", "group": "Ungrouped variables", "definition": "random(0..90#5 except [0,45,90])", "description": "", "templateType": "anything", "can_override": false}, "x1": {"name": "x1", "group": "Ungrouped variables", "definition": "random(10..300#10 except m2)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["x2", "y2", "d2", "m2", "x1", "mat2", "mat1", "mr", "dr"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "information", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "Sketch a diagram to help you understand the situation.
"}, {"type": "matrix", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "Write the vector $F_1$ in component form.
", "correctAnswer": "{mat1}", "correctAnswerFractions": false, "numRows": "2", "numColumns": 1, "allowResize": false, "tolerance": "0", "markPerCell": false, "allowFractions": false, "minColumns": 1, "maxColumns": 0, "minRows": 1, "maxRows": 0, "prefilledCells": ""}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "Calculate the horizontal component of vector $F_2$, in Newtons.
", "minValue": "{x2}", "maxValue": "{x2}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "precisionType": "dp", "precision": "1", "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": true, "showPrecisionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "Calculate the vertical component of vector $F_2$, in Newtons.
", "minValue": "{y2}", "maxValue": "{y2}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "precisionType": "dp", "precision": "1", "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": true, "showPrecisionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "matrix", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "Now write vector $F_2$ in component form.
", "correctAnswer": "{mat2}", "correctAnswerFractions": false, "numRows": "2", "numColumns": 1, "allowResize": false, "tolerance": "0", "markPerCell": false, "allowFractions": false, "minColumns": 1, "maxColumns": 0, "minRows": 1, "maxRows": 0, "prefilledCells": "", "precisionType": "dp", "precision": "1", "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": true}, {"type": "matrix", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "Calculate the resultant vector $F_r$ of the two vectors $F_1$ and $F_2$.
", "stepsPenalty": 0, "steps": [{"type": "information", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "The resultant of two vectors is calculated by adding them together. Refer to Lesson 2 for examples.
"}], "correctAnswer": "{mat1+mat2}", "correctAnswerFractions": false, "numRows": "2", "numColumns": 1, "allowResize": false, "tolerance": "0", "markPerCell": false, "allowFractions": false, "minColumns": 1, "maxColumns": 0, "minRows": 1, "maxRows": 0, "prefilledCells": "", "precisionType": "dp", "precision": "1", "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": true}, {"type": "quantity", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "Calculate the magnitude of the resultant force $F_r$, correct to the nearest whole number.
", "alternatives": [{"type": "quantity", "useCustomName": false, "customName": "", "marks": "0.5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "alternativeFeedbackMessage": "Incorrect or missing unit.
", "useAlternativeFeedback": false, "settings": {"correctAnswer": "qty(mr,\"N\")", "hint": "remind units", "allow_unitless": false, "incompatible_units_action": "convert", "different_units_action": "convert", "different_units_penalty": "0", "wiggle": "1"}}], "settings": {"correctAnswer": "qty(mr,\"N\")", "hint": "remind units", "allow_unitless": false, "incompatible_units_action": "incorrect", "different_units_action": "convert", "different_units_penalty": "0", "wiggle": "1"}}, {"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "Calculate the direction of the resultant force $F_r$, in degrees from horizontal.
\n[[0]]$^\\circ$
", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "alternatives": [{"type": "numberentry", "useCustomName": true, "customName": "Inaccurate", "marks": "0.5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "alternativeFeedbackMessage": "Poor rounding or inaccurate answer.
", "useAlternativeFeedback": false, "minValue": "{dr}-1", "maxValue": "{dr}+1", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "precisionType": "dp", "precision": 0, "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": true, "showPrecisionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": true, "customName": "90-", "marks": "0.5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "alternativeFeedbackMessage": "Wrong orientation. Angle should be given from horizontal.
", "useAlternativeFeedback": false, "minValue": "90-{dr}", "maxValue": "90-{dr}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "precisionType": "dp", "precision": 0, "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": true, "showPrecisionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "minValue": "{dr}", "maxValue": "{dr}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "precisionType": "dp", "precision": 0, "precisionPartialCredit": 0, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": true, "showPrecisionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}]}], "showstudentname": true, "duration": 3600, "name": "Stephen's copy of Vectors", "showQuestionGroupNames": false, "feedback": {"showactualmark": true, "intro": "", "showtotalmark": true, "allowrevealanswer": true, "advicethreshold": 0, "feedbackmessages": [], "showanswerstate": true, "enterreviewmodeimmediately": true, "showexpectedanswerswhen": "inreview", "showpartfeedbackmessageswhen": "always", "showactualmarkwhen": "always", "showtotalmarkwhen": "always", "showanswerstatewhen": "always", "showadvicewhen": "never"}, "percentPass": "75", "type": "exam", "contributors": [{"name": "Martin Jones", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/145/"}, {"name": "Stephen Face", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2553/"}], "extensions": ["quantities"], "custom_part_types": [{"source": {"pk": 7, "author": {"name": "Christian Lawson-Perfect", "pk": 7}, "edit_page": "/part_type/7/edit"}, "name": "Quantity with units", "short_name": "quantity", "description": "The student enters a quantity with units.
", "help_url": "https://github.com/numbas/numbas-extension-quantities", "input_widget": "string", "input_options": {"correctAnswer": "plain_string(settings[\"correctAnswer\"])", "hint": {"static": false, "value": "switch(\n settings[\"hint\"]=\"remind units\",\n \"Include units in your answer.\",\n settings[\"hint\"]=\"show units\",\n \"Give your answer in \"+units_string(settings[\"correctAnswer\"])\n ,\n \"\"\n)"}, "allowEmpty": {"static": true, "value": false}}, "can_be_gap": true, "can_be_step": true, "marking_script": "mark:\napply(valid_number);\napply(student_quantity);\napply(has_units);\napply(compatible);\ntry(\n correctif(close_enough),\n x,\n apply(student_quantity)\n);\napply(same_units)\n\ninterpreted_answer:\nstudent_quantity\n\nallowed_notation_styles:\n[\"plain\",\"en\"]\n\nmatch_student_number:\nmatchnumber(studentAnswer,allowed_notation_styles)\n\nstudent_number:\nmatch_student_number[1]\n\nraw_student_units:\ntry(\n quantity(studentAnswer[len(match_student_number[0])..len(studentAnswer)]),\n message,\n warn(\"Your answer is not a valid quantity.\");\n fail(\"Your answer is not a valid quantity.\")\n)\n\nstudent_units:\nif(compatible(raw_student_units,correct_units) or settings[\"incompatible_units_action\"]<>\"convert\",\n raw_student_units,\n correct_units\n)\n\nstudent_quantity:\napply(student_units);\ntry(\n student_number * student_units,\n message,\n warn(\"Your answer is not a valid quantity.\");\n fail(\"Your answer is not a valid quantity.\")\n)\n\ncorrect_quantity:\nsettings[\"correctAnswer\"]\n\ncompatible:\nif(compatible(raw_student_units,correct_quantity),\n true\n,\n let(message,\"Your answer does not have the correct dimensions.\",\n if(settings[\"incompatible_units_action\"]=\"prevent\",\n warn(message);\n fail(message)\n ,\n if(settings[\"incompatible_units_action\"]=\"convert\",\n incorrect(\"Your answer does not have the correct dimensions. It will be marked as if the correct dimensions were used, and then a penalty will be applied.\")\n ,\n incorrect(\"Your answer does not have the correct dimensions.\");\n end()\n )\n );\n false\n )\n)\n\ncorrect_units:\nunits(correct_quantity)\n\nsame_units:\nassert(raw_student_units=correct_units,\n let(\n message,if(settings[\"hint\"]=\"show units\",\"You did not give your answer in \"+units_string(correct_units)+\".\", \"Your answer is not in the expected units.\"),\n switch(\n settings[\"different_units_action\"]=\"prevent\",\n warn(message);\n fail(message)\n ,\n settings[\"different_units_action\"]=\"incorrect\",\n incorrect(message); \n warn(message);\n end()\n ,\n settings[\"different_units_action\"]=\"warn\",\n warn(message);\n multiply_credit(1-settings[\"different_units_penalty\"],message)\n ,\n settings[\"different_units_penalty\"]<1,\n multiply_credit(1-settings[\"different_units_penalty\"],message)\n ,\n false\n )\n );\n false\n)\n\nhas_units:\nassert(not unitless(student_quantity),\n assert(settings[\"allow_unitless\"],\n warn(\"You must include the units in your answer.\");\n fail(\"You did not include units in your answer.\")\n )\n)\n\ncan_compare:\ncompatible or settings[\"incompatible_units_action\"]=\"convert\"\n\nclose_enough:\nif(can_compare,\n student_quantity>=correct_quantity - wiggle \n and \n student_quantity<=correct_quantity + wiggle \n,\n false\n)\n\nwiggle:\nunits(correct_quantity)*abs(eval(settings[\"wiggle\"]))\n\nvalid_number:\nif(isNaN(student_number),\n warn(translate(\"part.numberentry.answer invalid\"));\n fail(translate(\"part.numberentry.answer invalid\"))\n,\n true\n )", "marking_notes": [{"name": "mark", "description": "This is the main marking note. It should award credit and provide feedback based on the student's answer.", "definition": "apply(valid_number);\napply(student_quantity);\napply(has_units);\napply(compatible);\ntry(\n correctif(close_enough),\n x,\n apply(student_quantity)\n);\napply(same_units)"}, {"name": "interpreted_answer", "description": "A value representing the student's answer to this part.", "definition": "student_quantity"}, {"name": "allowed_notation_styles", "description": "", "definition": "[\"plain\",\"en\"]"}, {"name": "match_student_number", "description": "", "definition": "matchnumber(studentAnswer,allowed_notation_styles)"}, {"name": "student_number", "description": "The scalar part of the student's quantity
", "definition": "match_student_number[1]"}, {"name": "raw_student_units", "description": "The units of the student's quantity, before converting.
", "definition": "try(\n quantity(studentAnswer[len(match_student_number[0])..len(studentAnswer)]),\n message,\n warn(\"Your answer is not a valid quantity.\");\n fail(\"Your answer is not a valid quantity.\")\n)"}, {"name": "student_units", "description": "The units of the student's quantity.
\nIf the student used units incompatible with the units in the expected answer, and the \"what to do if incompatible units used\" option is set to \"mark as if correct units used\", the student's units are ignored and the expected units are used instead.
", "definition": "if(compatible(raw_student_units,correct_units) or settings[\"incompatible_units_action\"]<>\"convert\",\n raw_student_units,\n correct_units\n)"}, {"name": "student_quantity", "description": "The student's answer, interpreted as a quantity.
\nMarking fails if the student does not enter a valid quantity.
", "definition": "apply(student_units);\ntry(\n student_number * student_units,\n message,\n warn(\"Your answer is not a valid quantity.\");\n fail(\"Your answer is not a valid quantity.\")\n)"}, {"name": "correct_quantity", "description": "", "definition": "settings[\"correctAnswer\"]"}, {"name": "compatible", "description": "Are the units of the student's quantity compatible with the units of the expected quantity?
", "definition": "if(compatible(raw_student_units,correct_quantity),\n true\n,\n let(message,\"Your answer does not have the correct dimensions.\",\n if(settings[\"incompatible_units_action\"]=\"prevent\",\n warn(message);\n fail(message)\n ,\n if(settings[\"incompatible_units_action\"]=\"convert\",\n incorrect(\"Your answer does not have the correct dimensions. It will be marked as if the correct dimensions were used, and then a penalty will be applied.\")\n ,\n incorrect(\"Your answer does not have the correct dimensions.\");\n end()\n )\n );\n false\n )\n)"}, {"name": "correct_units", "description": "", "definition": "units(correct_quantity)"}, {"name": "same_units", "description": "/Are the student's quantity and the expected quantity in exactly the same units?
", "definition": "assert(raw_student_units=correct_units,\n let(\n message,if(settings[\"hint\"]=\"show units\",\"You did not give your answer in \"+units_string(correct_units)+\".\", \"Your answer is not in the expected units.\"),\n switch(\n settings[\"different_units_action\"]=\"prevent\",\n warn(message);\n fail(message)\n ,\n settings[\"different_units_action\"]=\"incorrect\",\n incorrect(message); \n warn(message);\n end()\n ,\n settings[\"different_units_action\"]=\"warn\",\n warn(message);\n multiply_credit(1-settings[\"different_units_penalty\"],message)\n ,\n settings[\"different_units_penalty\"]<1,\n multiply_credit(1-settings[\"different_units_penalty\"],message)\n ,\n false\n )\n );\n false\n)"}, {"name": "has_units", "description": "", "definition": "assert(not unitless(student_quantity),\n assert(settings[\"allow_unitless\"],\n warn(\"You must include the units in your answer.\");\n fail(\"You did not include units in your answer.\")\n )\n)"}, {"name": "can_compare", "description": "Can the student's answer be compared with the correct answer? True if compatible units used, or \"mark as if correct units used\" selected.
", "definition": "compatible or settings[\"incompatible_units_action\"]=\"convert\""}, {"name": "close_enough", "description": "Is the student's quantity within the allowed tolerance of the expected answer?
", "definition": "if(can_compare,\n student_quantity>=correct_quantity - wiggle \n and \n student_quantity<=correct_quantity + wiggle \n,\n false\n)"}, {"name": "wiggle", "description": "", "definition": "units(correct_quantity)*abs(eval(settings[\"wiggle\"]))"}, {"name": "valid_number", "description": "Is the scalar part of the student's answer a valid number?
", "definition": "if(isNaN(student_number),\n warn(translate(\"part.numberentry.answer invalid\"));\n fail(translate(\"part.numberentry.answer invalid\"))\n,\n true\n )\n"}], "settings": [{"name": "correctAnswer", "label": "Correct answer", "help_url": "", "hint": "The expected quantity.", "input_type": "code", "default_value": "", "evaluate": true}, {"name": "hint", "label": "Input hint", "help_url": "", "hint": "", "input_type": "dropdown", "default_value": "remind units", "choices": [{"value": "none", "label": "None"}, {"value": "remind units", "label": "Remind to include units"}, {"value": "show units", "label": "Show required units"}]}, {"name": "allow_unitless", "label": "Allow unitless answer?", "help_url": "", "hint": "If not ticked, the student is prevented from submitting an answer without specifying units.", "input_type": "checkbox", "default_value": true}, {"name": "incompatible_units_action", "label": "What to do if incompatible units used", "help_url": "", "hint": "If the student's answer is given in units incompatible with the correct answer's units: