// Numbas version: finer_feedback_settings
{"name": "Cross product", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"metadata": {"description": "<p>Given vectors $\\boldsymbol{a,\\;b}$, find $\\boldsymbol{a\\times b}$</p>\n<p>rebelmaths</p>", "licence": "Creative Commons Attribution 4.0 International"}, "variables": {"d": {"description": "", "definition": "s4*random(2..9)", "group": "Ungrouped variables", "templateType": "anything", "name": "d"}, "c": {"description": "", "definition": "s3*random(2..9)", "group": "Ungrouped variables", "templateType": "anything", "name": "c"}, "b": {"description": "", "definition": "s2*random(2..9)", "group": "Ungrouped variables", "templateType": "anything", "name": "b"}, "s1": {"description": "", "definition": "random(1,-1)", "group": "Ungrouped variables", "templateType": "anything", "name": "s1"}, "f": {"description": "", "definition": "random(2..9)", "group": "Ungrouped variables", "templateType": "anything", "name": "f"}, "g": {"description": "", "definition": "s1*random(2..9)", "group": "Ungrouped variables", "templateType": "anything", "name": "g"}, "s5": {"description": "", "definition": "random(1,-1)", "group": "Ungrouped variables", "templateType": "anything", "name": "s5"}, "a": {"description": "", "definition": "s1*random(2..9)", "group": "Ungrouped variables", "templateType": "anything", "name": "a"}, "s2": {"description": "", "definition": "random(1,-1)", "group": "Ungrouped variables", "templateType": "anything", "name": "s2"}, "inner": {"description": "", "definition": "{a*c+b*d+f*g}", "group": "Ungrouped variables", "templateType": "anything", "name": "inner"}, "s3": {"description": "", "definition": "random(1,-1)", "group": "Ungrouped variables", "templateType": "anything", "name": "s3"}, "s4": {"description": "", "definition": "random(1,-1)", "group": "Ungrouped variables", "templateType": "anything", "name": "s4"}}, "advice": "<p>\\[ \\begin{eqnarray*} \\boldsymbol{a\\times b}&amp;=&amp; \\begin{vmatrix} \\boldsymbol{i} &amp; \\boldsymbol{j} &amp;\\boldsymbol{k}\\\\ \\var{a} &amp; \\var{b} &amp; \\var{g}\\\\ \\var{c} &amp; \\var{d} &amp; \\var{f} \\end{vmatrix}\\\\ \\\\ &amp;=&amp;\\simplify[zeroterm]{({b}*{f}-{g}*{d})v:i - ({a}*{f}-{g}*{c} )v:j+({a}*{d}-{b}*{c})v:k}\\\\ \\\\ &amp;=&amp;\\simplify[std]{{b*f-g*d}v:i+{g*c-a*f}v:j+{a*d-b*c}v:k} \\end{eqnarray*} \\]</p>", "ungrouped_variables": ["a", "c", "b", "d", "g", "f", "s3", "s2", "s1", "s5", "s4", "inner"], "name": "Cross product", "rulesets": {"std": ["all", "fractionNumbers", "!collectNumbers", "!noLeadingMinus"]}, "preamble": {"css": "", "js": ""}, "tags": [], "variable_groups": [], "statement": "<p>Given the vectors:<br/>\\[{\\bf a}=\\simplify{{a} v:i+{b}v:j+{g}v:k},\\;\\;\\;{\\bf b}=\\simplify[std]{{c}v:i+{d}v:j+{f}v:k}\\]</p>\n<p>answer the following question:</p>", "variablesTest": {"condition": "", "maxRuns": 100}, "parts": [{"type": "gapfill", "marks": 0, "gaps": [{"correctAnswerFraction": false, "marks": 6, "unitTests": [], "variableReplacementStrategy": "originalfirst", "maxValue": "{b*f-g*d}", "showCorrectAnswer": true, "showFeedbackIcon": true, "mustBeReducedPC": 0, "customMarkingAlgorithm": "", "minValue": "{b*f-g*d}", "mustBeReduced": false, "correctAnswerStyle": "plain", "notationStyles": ["plain", "en", "si-en"], "type": "numberentry", "variableReplacements": [], "scripts": {}, "extendBaseMarkingAlgorithm": true, "allowFractions": false}, {"correctAnswerFraction": false, "marks": 6, "unitTests": [], "variableReplacementStrategy": "originalfirst", "maxValue": "{g*c-a*f}", "showCorrectAnswer": true, "showFeedbackIcon": true, "mustBeReducedPC": 0, "customMarkingAlgorithm": "", "minValue": "{g*c-a*f}", "mustBeReduced": false, "correctAnswerStyle": "plain", "notationStyles": ["plain", "en", "si-en"], "type": "numberentry", "variableReplacements": [], "scripts": {}, "extendBaseMarkingAlgorithm": true, "allowFractions": false}, {"correctAnswerFraction": false, "marks": 6, "unitTests": [], "variableReplacementStrategy": "originalfirst", "maxValue": "{a*d-b*c}", "showCorrectAnswer": true, "showFeedbackIcon": true, "mustBeReducedPC": 0, "customMarkingAlgorithm": "", "minValue": "{a*d-b*c}", "mustBeReduced": false, "correctAnswerStyle": "plain", "notationStyles": ["plain", "en", "si-en"], "type": "numberentry", "variableReplacements": [], "scripts": {}, "extendBaseMarkingAlgorithm": true, "allowFractions": false}], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "showFeedbackIcon": true, "prompt": "<p>Find ${{\\bf a}\\times {\\bf b}} =\\;\\;$ [[0]]${\\bf i}+ $[[1]]${\\bf j}+ $[[2]]${\\bf k}$</p>", "customMarkingAlgorithm": "", "unitTests": [], "sortAnswers": false, "variableReplacements": [], "scripts": {}, "extendBaseMarkingAlgorithm": true}], "extensions": [], "functions": {}, "type": "question", "contributors": [{"name": "Julie Crowley", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/113/"}, {"name": "Clodagh Carroll", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/384/"}, {"name": "Marie Nicholson", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1799/"}, {"name": "Simon Thomas", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3148/"}]}]}], "contributors": [{"name": "Julie Crowley", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/113/"}, {"name": "Clodagh Carroll", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/384/"}, {"name": "Marie Nicholson", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1799/"}, {"name": "Simon Thomas", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3148/"}]}