// Numbas version: exam_results_page_options
{"name": "Numbastest 1: Vektorer, skalarprodukt og parametrisering av kurver", "metadata": {"description": "<p>Numbastest forelesning 1 og 2, uke 2</p>", "licence": "All rights reserved"}, "duration": 1200, "percentPass": 0, "showQuestionGroupNames": false, "shuffleQuestionGroups": false, "showstudentname": true, "question_groups": [{"name": "Group", "pickingStrategy": "all-ordered", "pickQuestions": 1, "questionNames": ["", "", "", "", "", "", "", "", ""], "variable_overrides": [[], [], [], [], [], [], [], [], []], "questions": [{"name": "Lengden av vektor", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Elena Malyutina", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7213/"}], "tags": [], "metadata": {"description": "", "licence": "None specified"}, "statement": "<p>Finn lengden av vektor $a=(\\var{a},\\var{b},\\var{c})$</p>", "advice": "", "rulesets": {}, "variables": {"a": {"name": "a", "group": "Ungrouped variables", "definition": "random(-5 .. 5#1)", "description": "", "templateType": "randrange"}, "b": {"name": "b", "group": "Ungrouped variables", "definition": "random(-5 .. 5#1)", "description": "", "templateType": "randrange"}, "c": {"name": "c", "group": "Ungrouped variables", "definition": "random(-5 .. 5#1)", "description": "", "templateType": "randrange"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["a", "b", "c"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "jme", "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": "<p>$\\|a\\|=$</p>", "answer": "sqrt({a^2+b^2+c^2})", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "valuegenerators": []}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "Summen av vektorer", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Elena Malyutina", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7213/"}], "tags": [], "metadata": {"description": "", "licence": "None specified"}, "statement": "<p>Finn summen av vektorene $a=(\\var{a},\\var{b},\\var{c})$ og $b=(\\var{d},\\var{f},\\var{g})$</p>", "advice": "", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"a": {"name": "a", "group": "Ungrouped variables", "definition": "random(-20 .. 20#1)", "description": "", "templateType": "randrange", "can_override": false}, "b": {"name": "b", "group": "Ungrouped variables", "definition": "random(-20 .. 20#1)", "description": "", "templateType": "randrange", "can_override": false}, "c": {"name": "c", "group": "Ungrouped variables", "definition": "random(-20 .. 20#1)", "description": "", "templateType": "randrange", "can_override": false}, "d": {"name": "d", "group": "Ungrouped variables", "definition": "random(-20 .. 20#1)", "description": "", "templateType": "randrange", "can_override": false}, "f": {"name": "f", "group": "Ungrouped variables", "definition": "random(-20 .. 20#1)", "description": "", "templateType": "randrange", "can_override": false}, "g": {"name": "g", "group": "Ungrouped variables", "definition": "random(-20 .. 20#1)", "description": "", "templateType": "randrange", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["a", "b", "c", "d", "f", "g"], "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>Den f&oslash;rste koordinaten er&nbsp;[[0]]</p>\n<p>Den&nbsp;andre koordinaten er&nbsp;[[1]]</p>\n<p>Den&nbsp;tredje koordinaten er&nbsp;[[2]]</p>", "gaps": [{"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{a+d}", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": []}, {"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{b+f}", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": []}, {"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{c+g}", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": []}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "Skalar produkt", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Elena Malyutina", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7213/"}], "tags": [], "metadata": {"description": "", "licence": "None specified"}, "statement": "<p>Finn skalarproduktet av $a=(\\var{a},\\var{b},\\var{c})$ og $b=(\\var{d},\\var{f},\\var{g})$</p>", "advice": "", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"a": {"name": "a", "group": "Ungrouped variables", "definition": "random(-10 .. 10#1)", "description": "", "templateType": "randrange", "can_override": false}, "b": {"name": "b", "group": "Ungrouped variables", "definition": "random(-10 .. 10#1)", "description": "", "templateType": "randrange", "can_override": false}, "c": {"name": "c", "group": "Ungrouped variables", "definition": "random(-10 .. 10#1)", "description": "", "templateType": "randrange", "can_override": false}, "d": {"name": "d", "group": "Ungrouped variables", "definition": "random(-10 .. 10#1)", "description": "", "templateType": "randrange", "can_override": false}, "f": {"name": "f", "group": "Ungrouped variables", "definition": "random(-10 .. 10#1)", "description": "", "templateType": "randrange", "can_override": false}, "g": {"name": "g", "group": "Ungrouped variables", "definition": "random(-10 .. 10#1)", "description": "", "templateType": "randrange", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["a", "b", "c", "d", "f", "g"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "jme", "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": "<p>$a\\cdot b=$</p>", "answer": "{a*d+b*f+c*g}", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": []}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "Vinkel mellom vektorene", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Elena Malyutina", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7213/"}], "tags": [], "metadata": {"description": "", "licence": "None specified"}, "statement": "<p>Finn vinkel mellom&nbsp;vektorene&nbsp;$a$ og&nbsp;$b$ (skriv inn vinkelen i grader)</p>", "advice": "", "rulesets": {}, "variables": {"a": {"name": "a", "group": "Ungrouped variables", "definition": "random(-9 .. 9#2)", "description": "", "templateType": "randrange"}, "b": {"name": "b", "group": "Ungrouped variables", "definition": "random(-10 .. 10#1)", "description": "", "templateType": "randrange"}, "c": {"name": "c", "group": "Ungrouped variables", "definition": "random(-10 .. 10#1)", "description": "", "templateType": "randrange"}, "d": {"name": "d", "group": "Ungrouped variables", "definition": "random(-10 .. 10#1)", "description": "", "templateType": "randrange"}, "f": {"name": "f", "group": "Ungrouped variables", "definition": "random(-10 .. 10#1)", "description": "", "templateType": "randrange"}, "g": {"name": "g", "group": "Ungrouped variables", "definition": "random(1 .. 10#1)", "description": "", "templateType": "randrange"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["a", "b", "c", "d", "f", "g"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "jme", "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": "<p>$a=(\\var{a},\\var{b},2)$ og&nbsp;$b=(\\var{d},\\var{f},\\var{-(a*d+b*f)/2})$</p>", "answer": "90", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "valuegenerators": []}, {"type": "jme", "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": "<p>$a=(\\var{a},0,0)$ og&nbsp;$b=(\\var{g*abs(a)/a},0,\\var{g})$</p>", "answer": "45", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "valuegenerators": []}, {"type": "jme", "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": "<p>$a=(\\var{a},0,0)$ og&nbsp;$b=(\\dfrac{\\var{g*abs(a)/a}}{\\sqrt{3}},\\var{g},0)$</p>", "answer": "60", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "valuegenerators": []}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "Projeksjon", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Elena Malyutina", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7213/"}], "tags": [], "metadata": {"description": "", "licence": "None specified"}, "statement": "<p>Finn projeksjoner av $a=(\\var{a},\\var{b},\\var{c})$ og $b=(\\var{d},\\var{f},\\var{g})$</p>", "advice": "", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"a": {"name": "a", "group": "Ungrouped variables", "definition": "random(-10 .. 10#1)", "description": "", "templateType": "randrange", "can_override": false}, "b": {"name": "b", "group": "Ungrouped variables", "definition": "random(-10 .. 10#1)", "description": "", "templateType": "randrange", "can_override": false}, "c": {"name": "c", "group": "Ungrouped variables", "definition": "random(-10 .. 10#1)", "description": "", "templateType": "randrange", "can_override": false}, "d": {"name": "d", "group": "Ungrouped variables", "definition": "random(-10 .. 10#1)", "description": "", "templateType": "randrange", "can_override": false}, "f": {"name": "f", "group": "Ungrouped variables", "definition": "random(-9 .. 9#2)", "description": "", "templateType": "randrange", "can_override": false}, "g": {"name": "g", "group": "Ungrouped variables", "definition": "random(-9 .. 9#2)", "description": "", "templateType": "randrange", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["a", "b", "c", "d", "f", "g"], "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>$proj_a b=$</p>\n<p>Den f&oslash;rste koordinaten er&nbsp;[[0]]</p>\n<p>Den andre koordinaten er&nbsp;[[1]]</p>\n<p>Den tredje koordinaten er&nbsp;[[2]]</p>", "gaps": [{"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{(a*d+b*f+c*g)/(a^2+b^2+c^2)*a}", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": []}, {"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{(a*d+b*f+c*g)/(a^2+b^2+c^2)*b}", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": []}, {"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{(a*d+b*f+c*g)/(a^2+b^2+c^2)*c}", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": []}], "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>$proj_b a=$</p>\n<p>Den f&oslash;rste koordinaten er&nbsp;[[0]]</p>\n<p>Den andre koordinaten er&nbsp;[[1]]</p>\n<p>Den tredje koordinaten er&nbsp;[[2]]</p>", "gaps": [{"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{(a*d+b*f+c*g)/(d^2+f^2+g^2)*d}", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": []}, {"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{(a*d+b*f+c*g)/(d^2+f^2+g^2)*f}", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": []}, {"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{(a*d+b*f+c*g)/(d^2+f^2+g^2)*g}", "showPreview": true, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": []}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "Vektorer med samme retning", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Elena Malyutina", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7213/"}], "tags": [], "metadata": {"description": "", "licence": "None specified"}, "statement": "<p>Velg alle vektorer som har samme retning som vektor $a=(\\var{a},\\var{b},\\var{c})$</p>", "advice": "", "rulesets": {}, "variables": {"a": {"name": "a", "group": "Ungrouped variables", "definition": "random(-10 .. 10#2)", "description": "", "templateType": "randrange"}, "b": {"name": "b", "group": "Ungrouped variables", "definition": "random(-10 .. 10#2)", "description": "", "templateType": "randrange"}, "c": {"name": "c", "group": "Ungrouped variables", "definition": "random(-10 .. 10#2)", "description": "", "templateType": "randrange"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["a", "b", "c"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "m_n_2", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minMarks": 0, "maxMarks": 0, "shuffleChoices": false, "displayType": "checkbox", "displayColumns": 0, "minAnswers": 0, "maxAnswers": 0, "warningType": "none", "showCellAnswerState": true, "choices": ["$(\\var{-3a}, \\var{-3b}, \\var{-3c})$", "$(\\var{3a/2}, \\var{3b/2}, \\var{3c/2})$", "$(\\var{a/2}, \\var{b/2}, \\var{c/2})$", "$(\\var{-a/2}, \\var{-b/2}, \\var{-c/2})$", "$(\\var{-a}, \\var{-b}, \\var{-c})$"], "matrix": ["-1", "1", "1", "-1", "-1"], "distractors": ["", "", "", "", ""]}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "Vektorer med motsatt retning", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Elena Malyutina", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7213/"}], "tags": [], "metadata": {"description": "", "licence": "None specified"}, "statement": "<p>Velg alle vektorer som har&nbsp;motsatt retning&nbsp;med vektor $a=(\\var{a},\\var{b},\\var{c})$</p>", "advice": "", "rulesets": {}, "variables": {"a": {"name": "a", "group": "Ungrouped variables", "definition": "random(-10 .. 10#2)", "description": "", "templateType": "randrange"}, "b": {"name": "b", "group": "Ungrouped variables", "definition": "random(-10 .. 10#2)", "description": "", "templateType": "randrange"}, "c": {"name": "c", "group": "Ungrouped variables", "definition": "random(-10 .. 10#2)", "description": "", "templateType": "randrange"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["a", "b", "c"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "m_n_2", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minMarks": 0, "maxMarks": 0, "shuffleChoices": false, "displayType": "checkbox", "displayColumns": 0, "minAnswers": 0, "maxAnswers": 0, "warningType": "none", "showCellAnswerState": true, "choices": ["$(\\var{-3a}, \\var{-3b}, \\var{-3c})$", "$(\\var{3a/2}, \\var{3b/2}, \\var{3c/2})$", "$(\\var{a/2}, \\var{b/2}, \\var{c/2})$", "$(\\var{-a/2}, \\var{-b/2}, \\var{-c/2})$", "$(\\var{-a}, \\var{-b}, \\var{-c})$", "$(\\var{-2a}, \\var{-b/2}, \\var{-c})$"], "matrix": ["1", "-1", "-1", "1", "1", "-1"], "distractors": ["", "", "", "", "", ""]}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "Parameterframstilling til en rett linje", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Ida Friestad Pedersen", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/792/"}, {"name": "Elena Malyutina", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7213/"}], "tags": [], "metadata": {"description": "", "licence": "None specified"}, "statement": "<p>En rett linje er gitt med parameterframstillingen&nbsp; $\\begin{array}{cccc} x &amp;= &amp;\\simplify[!noLeadingMinus, unitFactor]{ {a}&nbsp; +&nbsp; t }\\\\ y&amp;= &amp;\\simplify[!noLeadingMinus, unitFactor]{ {b} +&nbsp; {f}t }\\\\ z&amp;=&amp; \\simplify[!noLeadingMinus, unitFactor]{ {c}&nbsp; +&nbsp; {g}t} \\end{array}$</p>", "advice": "", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"a": {"name": "a", "group": "Ungrouped variables", "definition": "random(-10 .. 10#1)", "description": "", "templateType": "randrange", "can_override": false}, "b": {"name": "b", "group": "Ungrouped variables", "definition": "random(-9 .. 9#2)", "description": "", "templateType": "randrange", "can_override": false}, "c": {"name": "c", "group": "Ungrouped variables", "definition": "random(-10 .. 10#1)", "description": "", "templateType": "randrange", "can_override": false}, "d": {"name": "d", "group": "Ungrouped variables", "definition": "random(-9 .. 9#2)", "description": "", "templateType": "randrange", "can_override": false}, "f": {"name": "f", "group": "Ungrouped variables", "definition": "random(-10 .. 10#1)", "description": "", "templateType": "randrange", "can_override": false}, "g": {"name": "g", "group": "Ungrouped variables", "definition": "random(-10 .. 10#1)", "description": "", "templateType": "randrange", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["a", "b", "c", "d", "f", "g"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "m_n_2", "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>Avgj&oslash;r hvilke av disse punktene som ligger p&aring; denne linja</p>", "minMarks": 0, "maxMarks": 0, "shuffleChoices": true, "displayType": "checkbox", "displayColumns": 0, "minAnswers": 0, "maxAnswers": 0, "warningType": "none", "showCellAnswerState": true, "markingMethod": "sum ticked cells", "choices": ["$(\\var{a},\\var{b},\\var{c})$", "$(\\var{a+1},\\var{b+f},\\var{c+g})$", "$(\\var{a+2},\\var{-b+2*f},\\var{-c+2*g})$", "$(\\var{a+3},\\var{b+3*f},\\var{-c+3*g})$"], "matrix": ["1", "1", "-1", "-1"], "distractors": ["", "", "", ""]}, {"type": "m_n_2", "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>Avgj&oslash;r hvilke av disse vektorene som er retningsvektorene til denne linja</p>", "minMarks": 0, "maxMarks": 0, "shuffleChoices": true, "displayType": "checkbox", "displayColumns": 0, "minAnswers": 0, "maxAnswers": 0, "warningType": "none", "showCellAnswerState": true, "markingMethod": "sum ticked cells", "choices": ["$\\simplify[!noLeadingMinus, unitFactor]{i+({f}j)+({g}k)}$", "$\\simplify[!noLeadingMinus, unitFactor, simplifyFractions, unitDenominator]{-1/2 i-{f}/2 j-{g}/2 k}$", "$\\simplify[!noLeadingMinus, unitFactor, simplifyFractions, unitDenominator]{3/2 i-{3*f}/2 j-{3*g}/2 k}$", "$(-1,\\var{-f},\\var{-g})$"], "matrix": ["1", "1", "-1", "1"], "distractors": ["", "", "", ""]}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}, {"name": "Posisjon av to linjer", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Elena Malyutina", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7213/"}, {"name": "Glen Wilson", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/21835/"}], "tags": [], "metadata": {"description": "", "licence": "None specified"}, "statement": "<p>To linjer er gitt med parameterframstillingene&nbsp; &nbsp;$l_1:&nbsp; \\begin{array}{cccc} x= &amp; a_1 &amp; + &amp;u_1t \\\\ y= &amp; a_2 &amp; + &amp; u_2 t \\\\ z= &amp; a_3 &amp; + &amp; u_3t \\end{array}$&nbsp; &nbsp; &nbsp; og&nbsp; &nbsp; &nbsp; &nbsp;$l_2:&nbsp; \\begin{array}{cccc} x= &amp; b_1 &amp; + &amp;v_1s \\\\ y= &amp; b_2 &amp; + &amp; v_2 s \\\\ z= &amp; b_3 &amp; + &amp; v_3s \\end{array}$</p>\n<p>Man lager et system med tre likninger&nbsp;\\begin{array}{ccccccc} &amp;&nbsp;a_1&nbsp;&amp; + &amp; u_1t &amp; = &amp; b_1 &amp; + &amp; v_1s \\\\ &amp;&nbsp;a_2 &amp; + &amp; u_2t &amp; = &amp; b_2 &amp; + &amp; v_2s \\\\ &amp;&nbsp;a_3 &amp; + &amp; u_3t &amp; = &amp; b_3 &amp; + &amp; v_3s \\end{array}&nbsp;</p>\n<p>og l&oslash;ser det.</p>", "advice": "", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": [], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "m_n_x", "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>Finn ut hvordan linjene $l_1$ og $l_2$ ligger i forhold til hverandre, hvis</p>", "minMarks": 0, "maxMarks": 0, "minAnswers": 0, "maxAnswers": 0, "shuffleChoices": false, "shuffleAnswers": false, "displayType": "radiogroup", "warningType": "none", "showCellAnswerState": true, "markingMethod": "sum ticked cells", "choices": ["Systemet har &eacute;n mulig l&oslash;sning for $t$ og $s$<br/>$\\ \\ $", "Systemet har uendelig antall l&oslash;sninger for&nbsp;$t$ og $s$<br/>$\\ \\ $", "Systemet har&nbsp;ingen l&oslash;sning for&nbsp;$t$ og $s$&nbsp;<br/>og vektorene $(u_1,u_2,u_3)$ og $(v_1,v_2,v_3)$ er ikke parallelle<br/>$\\ \\ $", "Systemet har&nbsp;ingen l&oslash;sning&nbsp;<br/>og vektorene $(u_1,u_2,u_3)$ og $(v_1,v_2,v_3)$ er parallelle"], "matrix": [["0", "0", "0", "1"], ["1", "0", "0", "0"], ["0", "0", "1", "0"], ["0", "1", "0", "0"]], "layout": {"type": "all", "expression": ""}, "answers": ["$l_1$ og $l_2$ er sammenfallende", "$l_1$ og $l_2$ er parallelle", "$l_1$ og $l_2$ er&nbsp;vindskeive", "$l_1$ og $l_2$ skj&aelig;rer hverandre i ett punkt"]}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always"}]}], "allowPrinting": true, "navigation": {"allowregen": true, "reverse": true, "browse": true, "allowsteps": true, "showfrontpage": true, "showresultspage": 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