// 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": [{"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>", "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"}, "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"s4": {"group": "Ungrouped variables", "description": "", "definition": "random(1,-1)", "name": "s4", "templateType": "anything"}, "f": {"group": "Ungrouped variables", "description": "", "definition": "random(2..9)", "name": "f", "templateType": "anything"}, "c": {"group": "Ungrouped variables", "description": "", "definition": "s3*random(2..9)", "name": "c", "templateType": "anything"}, "inner": {"group": "Ungrouped variables", "description": "", "definition": "{a*c+b*d+f*g}", "name": "inner", "templateType": "anything"}, "g": {"group": "Ungrouped variables", "description": "", "definition": "s1*random(2..9)", "name": "g", "templateType": "anything"}, "s2": {"group": "Ungrouped variables", "description": "", "definition": "random(1,-1)", "name": "s2", "templateType": "anything"}, "a": {"group": "Ungrouped variables", "description": "", "definition": "s1*random(2..9)", "name": "a", "templateType": "anything"}, "d": {"group": "Ungrouped variables", "description": "", "definition": "s4*random(2..9)", "name": "d", "templateType": "anything"}, "b": {"group": "Ungrouped variables", "description": "", "definition": "s2*random(2..9)", "name": "b", "templateType": "anything"}, "s1": {"group": "Ungrouped variables", "description": "", "definition": "random(1,-1)", "name": "s1", "templateType": "anything"}, "s3": {"group": "Ungrouped variables", "description": "", "definition": "random(1,-1)", "name": "s3", "templateType": "anything"}, "s5": {"group": "Ungrouped variables", "description": "", "definition": "random(1,-1)", "name": "s5", "templateType": "anything"}}, "functions": {}, "tags": [], "extensions": [], "parts": [{"type": "gapfill", "scripts": {}, "extendBaseMarkingAlgorithm": true, "showFeedbackIcon": true, "gaps": [{"type": "numberentry", "scripts": {}, "extendBaseMarkingAlgorithm": true, "maxValue": "{b*f-g*d}", "showFeedbackIcon": true, "correctAnswerFraction": false, "correctAnswerStyle": "plain", "customMarkingAlgorithm": "", "mustBeReduced": false, "variableReplacementStrategy": "originalfirst", "minValue": "{b*f-g*d}", "allowFractions": false, "marks": 6, "mustBeReducedPC": 0, "variableReplacements": [], "notationStyles": ["plain", "en", "si-en"], "unitTests": [], "showCorrectAnswer": true}, {"type": "numberentry", "scripts": {}, "extendBaseMarkingAlgorithm": true, "maxValue": "{g*c-a*f}", "showFeedbackIcon": true, "correctAnswerFraction": false, "correctAnswerStyle": "plain", "customMarkingAlgorithm": "", "mustBeReduced": false, "variableReplacementStrategy": "originalfirst", "minValue": "{g*c-a*f}", "allowFractions": false, "marks": 6, "mustBeReducedPC": 0, "variableReplacements": [], "notationStyles": ["plain", "en", "si-en"], "unitTests": [], "showCorrectAnswer": true}, {"type": "numberentry", "scripts": {}, "extendBaseMarkingAlgorithm": true, "maxValue": "{a*d-b*c}", "showFeedbackIcon": true, "correctAnswerFraction": false, "correctAnswerStyle": "plain", "customMarkingAlgorithm": "", "mustBeReduced": false, "variableReplacementStrategy": "originalfirst", "minValue": "{a*d-b*c}", "allowFractions": false, "marks": 6, "mustBeReducedPC": 0, "variableReplacements": [], "notationStyles": ["plain", "en", "si-en"], "unitTests": [], "showCorrectAnswer": true}], "customMarkingAlgorithm": "", "prompt": "<p>Find ${{\\bf a}\\times {\\bf b}} =\\;\\;$ [[0]]${\\bf i}+ $[[1]]${\\bf j}+ $[[2]]${\\bf k}$</p>", "variableReplacementStrategy": "originalfirst", "sortAnswers": false, "marks": 0, "variableReplacements": [], "unitTests": [], "showCorrectAnswer": true}], "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[]{({b}*{f}-{g}*{d})v:i + ({g}*{c} - {a}*{f})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>", "name": "Cross product", "rulesets": {"std": ["all", "fractionNumbers", "!collectNumbers", "!noLeadingMinus"]}, "variable_groups": [], "preamble": {"css": "", "js": ""}, "ungrouped_variables": ["a", "c", "b", "d", "g", "f", "s3", "s2", "s1", "s5", "s4", "inner"], "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/"}]}]}], "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/"}]}