// Numbas version: exam_results_page_options
{"name": "VectorAnalysis", "extensions": [], "custom_part_types": [], "resources": [["question-resources/VectorAnalysis.png", "/srv/numbas/media/question-resources/VectorAnalysis.png"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "VectorAnalysis", "tags": [], "metadata": {"description": "", "licence": "None specified"}, "statement": "<p>In Figure 1, we have three randomly drawn vectors $\\vec{A}$, $\\vec{B}$ and $\\vec{C}$ with magnitudes $A$, $B$ and $C$ and angles with the horizontal direction $a$, $b$ and $c$ respectively.</p>\n<p></p>\n<p><img src=\"resources/question-resources/VectorAnalysis.png\" style=\"display: block; margin-left: auto; margin-right: auto;\" width=\"636\" height=\"334\"/></p>\n<p></p>\n<p>If $A=\\var{A}\\,\\mathrm{cm}$, $B=\\var{B}\\,\\mathrm{cm}$ and $C=\\var{C}\\,\\mathrm{cm}$</p>\n<p>and $a=\\var{aa[i]}\\,\\mathrm{^o}$, $b=\\var{bb[j]}\\,\\mathrm{^o}$ and $c=\\var{cc[k]}\\,\\mathrm{^o}$</p>\n<p>fill in the gaps below.</p>\n<p></p>\n<p>Use the following table:</p>\n<table style=\"height: 54px; width: 933px; border-style: solid; border-color: #000000; background-color: #c7f2ef; margin-left: auto; margin-right: auto;\">\n<tbody>\n<tr style=\"height: 18px;\">\n<th style=\"width: 127.95px; height: 18px; border-style: double; border-color: #080000; background-color: #1772e8; text-align: center;\" scope=\"row\">\n<p>angle($^o$)</p>\n</th>\n<th style=\"width: 102.317px; height: 18px; border-style: double; border-color: #080000; background-color: #1772e8; text-align: center;\" scope=\"row\">0</th>\n<th style=\"width: 150.383px; height: 18px; border-style: double; border-color: #080000; background-color: #1772e8; text-align: center;\" scope=\"row\">30</th>\n<th style=\"width: 150.383px; height: 18px; border-style: double; border-color: #080000; background-color: #1772e8; text-align: center;\" scope=\"row\">45</th>\n<th style=\"width: 150.383px; height: 18px; border-style: double; border-color: #080000; background-color: #1772e8; text-align: center;\" scope=\"row\">60</th>\n<th style=\"width: 112.15px; height: 18px; border-style: double; border-color: #080000; background-color: #1772e8; text-align: center;\" scope=\"row\">90</th>\n<th style=\"width: 150.383px; height: 18px; border-style: double; border-color: #080000; background-color: #1772e8; text-align: center;\" scope=\"row\">120</th>\n<th style=\"width: 141.65px; height: 18px; border-style: double; border-color: #080000; background-color: #1772e8; text-align: center;\" scope=\"row\">180</th>\n</tr>\n<tr style=\"height: 18px;\">\n<th style=\"width: 127.95px; height: 18px; border-style: double; border-color: #080101; text-align: center; vertical-align: middle; background-color: #1772e8;\" scope=\"col\">sin</th>\n<td style=\"width: 102.317px; height: 18px; text-align: center; vertical-align: middle; border-style: inset; border-color: #000000; background-color: #82b6ed;\">0</td>\n<td style=\"width: 150.383px; height: 18px; text-align: center; vertical-align: middle; border-style: inset; border-color: #000000; background-color: #82b6ed;\">$\\frac{1}{2}$</td>\n<td style=\"width: 150.383px; height: 18px; text-align: center; vertical-align: middle; border-style: inset; border-color: #000000; background-color: #82b6ed;\">$\\simplify{sqr(2)/2}$</td>\n<td style=\"width: 150.383px; height: 18px; text-align: center; vertical-align: middle; border-style: inset; border-color: #000000; background-color: #82b6ed;\">$\\simplify{sqr(3)/2}$</td>\n<td style=\"width: 112.15px; height: 18px; text-align: center; vertical-align: middle; border-style: inset; border-color: #000000; background-color: #82b6ed;\">1</td>\n<td style=\"width: 150.383px; height: 18px; text-align: center; vertical-align: middle; border-style: inset; border-color: #000000; background-color: #82b6ed;\">$\\simplify{sqr(3)/2}$</td>\n<td style=\"width: 141.65px; height: 18px; text-align: center; vertical-align: middle; border-style: inset; border-color: #000000; background-color: #82b6ed;\">0</td>\n</tr>\n<tr style=\"height: 18px;\">\n<th style=\"width: 127.95px; height: 18px; border-style: double; border-color: #080101; text-align: center; vertical-align: middle; background-color: #1772e8;\" scope=\"col\">cos</th>\n<td style=\"width: 102.317px; height: 18px; text-align: center; vertical-align: middle; border-style: inset; border-color: #000000; background-color: #82b6ed;\">1</td>\n<td style=\"width: 150.383px; height: 18px; text-align: center; vertical-align: middle; border-style: inset; border-color: #000000; background-color: #82b6ed;\">$\\simplify{sqr(3)/2}$</td>\n<td style=\"width: 150.383px; height: 18px; text-align: center; vertical-align: middle; border-style: inset; border-color: #000000; background-color: #82b6ed;\">$\\simplify{sqr(2)/2}$</td>\n<td style=\"width: 150.383px; height: 18px; text-align: center; vertical-align: middle; border-style: inset; border-color: #000000; background-color: #82b6ed;\">$\\frac{1}{2}$</td>\n<td style=\"width: 112.15px; height: 18px; text-align: center; vertical-align: middle; border-style: inset; border-color: #000000; background-color: #82b6ed;\">0</td>\n<td style=\"width: 150.383px; height: 18px; text-align: center; vertical-align: middle; border-style: inset; border-color: #000000; background-color: #82b6ed;\">-$\\frac{1}{2}$</td>\n<td style=\"width: 141.65px; height: 18px; text-align: center; vertical-align: middle; border-style: inset; border-color: #000000; background-color: #82b6ed;\">-1</td>\n</tr>\n</tbody>\n</table>\n<p>and round your answers to 2 decimal places.</p>\n<p></p>\n<p></p>", "advice": "", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"a": {"name": "a", "group": "Ungrouped variables", "definition": "random(1..20)", "description": "", "templateType": "anything", "can_override": false}, "aa": {"name": "aa", "group": "Ungrouped variables", "definition": "[0,30,45,60,90,120,180]", "description": "", "templateType": "anything", "can_override": false}, "b": {"name": "b", "group": "Ungrouped variables", "definition": "random(1..20)", "description": "", "templateType": "anything", "can_override": false}, "bb": {"name": "bb", "group": "Ungrouped variables", "definition": "[0,30,45,60,90,120,180]", "description": "", "templateType": "anything", "can_override": false}, "c": {"name": "c", "group": "Ungrouped variables", "definition": "random(1..20)", "description": "", "templateType": "anything", "can_override": false}, "cc": {"name": "cc", "group": "Ungrouped variables", "definition": "[0,30,45,60,90,120,180]", "description": "", "templateType": "anything", "can_override": false}, "i": {"name": "i", "group": "Ungrouped variables", "definition": "random(0..6)", "description": "", "templateType": "anything", "can_override": false}, "sinesA": {"name": "sinesA", "group": "Ungrouped variables", "definition": "[0,1/2,sqr(2)/2,sqr(3)/2,1,sqr(3)/2,0]", "description": "<p>The sine values of aa.</p>", "templateType": "anything", "can_override": false}, "cosinesA": {"name": "cosinesA", "group": "Ungrouped variables", "definition": "[1,sqr(3)/2,sqr(2)/2,1/2,0,-1/2,-1]", "description": "<p>The cosine values of aa.</p>", "templateType": "anything", "can_override": false}, "j": {"name": "j", "group": "Ungrouped variables", "definition": "random(0..6)", "description": "", "templateType": "anything", "can_override": false}, "k": {"name": "k", "group": "Ungrouped variables", "definition": "random(0..6)", "description": "", "templateType": "anything", "can_override": false}, "sinesB": {"name": "sinesB", "group": "Ungrouped variables", "definition": "[0,1/2,sqr(2)/2,sqr(3)/2,1,sqr(3)/2,0]", "description": "", "templateType": "anything", "can_override": false}, "cosinesB": {"name": "cosinesB", "group": "Ungrouped variables", "definition": "[1,sqr(3)/2,sqr(2)/2,1/2,0,-1/2,-1]", "description": "", "templateType": "anything", "can_override": false}, "sinesC": {"name": "sinesC", "group": "Ungrouped variables", "definition": "[0,1/2,sqr(2)/2,sqr(3)/2,1,sqr(3)/2,0]", "description": "", "templateType": "anything", "can_override": false}, "cosinesC": {"name": "cosinesC", "group": "Ungrouped variables", "definition": "[1,sqr(3)/2,sqr(2)/2,1/2,0,-1/2,-1]", "description": "", "templateType": "anything", "can_override": false}, "coeff1": {"name": "coeff1", "group": "Ungrouped variables", "definition": "random(2..10)", "description": "", "templateType": "anything", "can_override": false}, "coeff2": {"name": "coeff2", "group": "Ungrouped variables", "definition": "random(2..10)", "description": "", "templateType": "anything", "can_override": false}, "coeff3": {"name": "coeff3", "group": "Ungrouped variables", "definition": "random(2..10)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["a", "aa", "b", "bb", "c", "cc", "i", "sinesA", "cosinesA", "j", "k", "sinesB", "cosinesB", "sinesC", "cosinesC", "coeff1", "coeff2", "coeff3"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"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": "<p>Resolving $\\vec{A}$, $\\vec{B}$ and $\\vec{C}$ to their scalar components according to Fig. 2, we get</p>\n<p>i) $A_x$= [[0]] $\\,\\mathrm{cm}$ &nbsp;&nbsp;&nbsp; ii) $B_x$= [[2]] $\\,\\mathrm{cm}$&nbsp;&nbsp;&nbsp;&nbsp; iii) $C_x$= [[4]] $\\,\\mathrm{cm}$</p>\n<p>&nbsp;&nbsp; $A_y$= [[1]] $\\,\\mathrm{cm}$ &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; $B_y$= [[3]] $\\,\\mathrm{cm}$ &nbsp; &nbsp; &nbsp;&nbsp; &nbsp; $C_y$= [[5]] $\\,\\mathrm{cm}$</p>\n<p><em>(0.5 marks each)</em></p>", "stepsPenalty": "1", "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": "<p>Remember that for an angle $\\theta$ in a right triangle, by definition, $cos\\theta=\\frac{Adjacent Side}{Hypotenuse}$ while $sin\\theta=\\frac{Opposite Side}{Hypotenuse}$.</p>"}], "gaps": [{"type": "numberentry", "useCustomName": true, "customName": "Ax", "marks": "0.5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "precround({A}*{cosinesA[i]},2)", "maxValue": "precround({A}*{cosinesA[i]},2)", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": true, "customName": "Ay", "marks": "0.5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "precround({A}*{sinesA[i]},2)", "maxValue": "precround({A}*{sinesA[i]},2)", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": true, "customName": "Bx", "marks": "0.5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "precround({B}*{cosinesB[j]},2)", "maxValue": "precround({B}*{cosinesB[j]},2)", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": true, "customName": "By", "marks": "0.5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "precround({B}*{sinesB[j]},2)", "maxValue": "precround({B}*{sinesB[j]},2)", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": true, "customName": "Cx", "marks": "0.5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "precround({C}*{cosinesC[k]},2)", "maxValue": "precround({C}*{cosinesC[k]},2)", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": true, "customName": "Cy", "marks": "0.5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "precround({C}*{sinesC[k]},2)", "maxValue": "precround({C}*{sinesC[k]},2)", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}, {"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": "<p>If $\\vec{R}=\\var{coeff1}\\vec{A}-\\var{coeff2}\\vec{B}+\\var{coeff3}\\vec{C}$</p>\n<p>then in its vector component form, we will have:</p>\n<p>$\\vec{R}=$ [[0]]$\\hat{i}+$[[1]]$\\hat{j}$&nbsp; <em>(1.5 marks each)</em></p>\n<p>Use your answers from part (a) of this question.</p>", "stepsPenalty": "1", "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": "<p></p>\n<p>A vector $\\vec{A}$ in its vector component form is written as $A_x\\hat{i}+A_y\\hat{j}$.</p>"}], "gaps": [{"type": "numberentry", "useCustomName": true, "customName": "Rx", "marks": "1.5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{coeff1}*precround({A}*{cosinesA[i]},2)-{coeff2}*precround({B}*{cosinesB[j]},2)+{coeff3}*precround({C}*{cosinesC[k]},2)", "maxValue": "{coeff1}*precround({A}*{cosinesA[i]},2)-{coeff2}*precround({B}*{cosinesB[j]},2)+{coeff3}*precround({C}*{cosinesC[k]},2)", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": true, "customName": "Ry", "marks": "1.5", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{coeff1}*precround({A}*{sinesA[i]},2)-{coeff2}*precround({B}*{sinesB[j]},2)+{coeff3}*precround({C}*{sinesC[k]},2)", "maxValue": "{coeff1}*precround({A}*{sinesA[i]},2)-{coeff2}*precround({B}*{sinesB[j]},2)+{coeff3}*precround({C}*{sinesC[k]},2)", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "contributors": [{"name": "Konstantina Papadopoulou", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/19425/"}]}]}], "contributors": [{"name": "Konstantina Papadopoulou", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/19425/"}]}