// Numbas version: finer_feedback_settings
{"name": "Vectors: cross/vector product (2D)", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Vectors: cross/vector product (2D)", "tags": [], "metadata": {"description": "<p>Find the cross product of 2D vectors (WARNING: requires scalar answer (magnitude only))</p>", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "<p>Calculate the cross product below.&nbsp; Note that you are asked for a scalar answer; you should bear in mind that the true answer is a vector with this magnitude at right-angles to the 2D plane in which the original vectors lie.</p>", "advice": "<p>The cross-product of 2D vectors is calculated as follows.</p>\n<p>$$ \\begin{bmatrix} a_1 \\\\ a_2 \\end{bmatrix} \\times \\begin{bmatrix} b_1 \\\\ b_2 \\end{bmatrix}=a_1b_2-a_2b_1$$</p>\n<p>Hence the cross-product above is calculated as follows.</p>\n<p>$$ \\begin{bmatrix} \\var{A[0]} \\\\ \\var{A[1]} \\end{bmatrix} \\times \\begin{bmatrix} \\var{B[1]} \\\\ \\var{B[1]} \\end{bmatrix}=(\\var{A[0]}\\times\\var{B[1]})-(\\var{B[0]}\\times\\var{A[1]})=\\var{vectorProdMag}$$</p>", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {"A": {"name": "A", "group": "Ungrouped variables", "definition": "vector(random(-5..9 except 0),random(-3..5))", "description": "", "templateType": "anything", "can_override": false}, "B": {"name": "B", "group": "Ungrouped variables", "definition": "vector(random(-1..7),random(-1..6 except 0))", "description": "", "templateType": "anything", "can_override": false}, "vectorProd": {"name": "vectorProd", "group": "Ungrouped variables", "definition": "cross(vector(A[0],A[1],0),vector(B[0],B[1],0))", "description": "", "templateType": "anything", "can_override": false}, "vectorProdMag": {"name": "vectorProdMag", "group": "Ungrouped variables", "definition": "vectorProd[2]", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["A", "B", "vectorProd", "vectorProdMag"], "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>$\\var{A}\\times\\var{B}=$[[0]]</p>", "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, "minValue": "vectorProdMag", "maxValue": "vectorProdMag", "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": "Will Roberts", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/32402/"}], "resources": []}]}], "contributors": [{"name": "Will Roberts", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/32402/"}]}