// Numbas version: finer_feedback_settings
{"name": "Simon's copy of Cross product 1", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"extensions": [], "tags": [], "metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": "<p>Given vectors $\\boldsymbol{a,\\;b}$, find $\\boldsymbol{a\\times b}$</p>\n<p>rebelmaths</p>"}, "ungrouped_variables": ["a", "c", "b", "d", "g", "f", "s3", "s2", "s1", "s5", "s4", "inner"], "statement": "<p>Given the vectors:<br/>\\[\\boldsymbol{a}=\\simplify[std]{{a}v:i+{b}v:j+{g}v:k},\\;\\;\\;\\boldsymbol{b}=\\simplify[std]{{c}v:i+{d}v:j+{f}v:k}\\]</p>\n<p>answer the following question:</p>", "variablesTest": {"condition": "", "maxRuns": 100}, "variable_groups": [], "parts": [{"showCorrectAnswer": true, "prompt": "<p>Find $\\boldsymbol{a\\times b} =\\;\\;$ [[0]]$\\boldsymbol{i}$+[[1]]$\\boldsymbol{j}$+[[2]]$\\boldsymbol{k}$</p>", "variableReplacementStrategy": "originalfirst", "customMarkingAlgorithm": "", "sortAnswers": false, "type": "gapfill", "scripts": {}, "marks": 0, "unitTests": [], "gaps": [{"showCorrectAnswer": true, "minValue": "{b*f-g*d}", "variableReplacementStrategy": "originalfirst", "customMarkingAlgorithm": "", "mustBeReducedPC": 0, "type": "numberentry", "mustBeReduced": false, "correctAnswerFraction": false, "scripts": {}, "marks": "1", "correctAnswerStyle": "plain", "unitTests": [], "maxValue": "{b*f-g*d}", "notationStyles": ["plain", "en", "si-en"], "allowFractions": false, "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "showFeedbackIcon": true}, {"showCorrectAnswer": true, "minValue": "{g*c-a*f}", "variableReplacementStrategy": "originalfirst", "customMarkingAlgorithm": "", "mustBeReducedPC": 0, "type": "numberentry", "mustBeReduced": false, "correctAnswerFraction": false, "scripts": {}, "marks": "1", "correctAnswerStyle": "plain", "unitTests": [], "maxValue": "{g*c-a*f}", "notationStyles": ["plain", "en", "si-en"], "allowFractions": false, "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "showFeedbackIcon": true}, {"showCorrectAnswer": true, "minValue": "{a*d-b*c}", "variableReplacementStrategy": "originalfirst", "customMarkingAlgorithm": "", "mustBeReducedPC": 0, "type": "numberentry", "mustBeReduced": false, "correctAnswerFraction": false, "scripts": {}, "marks": "1", "correctAnswerStyle": "plain", "unitTests": [], "maxValue": "{a*d-b*c}", "notationStyles": ["plain", "en", "si-en"], "allowFractions": false, "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "showFeedbackIcon": true}], "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "showFeedbackIcon": true}], "name": "Simon's copy of Cross product 1", "rulesets": {"std": ["all", "fractionNumbers", "!collectNumbers", "!noLeadingMinus"]}, "functions": {}, "preamble": {"js": "", "css": ""}, "variables": {"inner": {"definition": "{a*c+b*d+f*g}", "group": "Ungrouped variables", "templateType": "anything", "description": "", "name": "inner"}, "s5": {"definition": "random(1,-1)", "group": "Ungrouped variables", "templateType": "anything", "description": "", "name": "s5"}, "c": {"definition": "s3*random(2..9)", "group": "Ungrouped variables", "templateType": "anything", "description": "", "name": "c"}, "a": {"definition": "s1*random(2..9)", "group": "Ungrouped variables", "templateType": "anything", "description": "", "name": "a"}, "d": {"definition": "s4*random(2..9)", "group": "Ungrouped variables", "templateType": "anything", "description": "", "name": "d"}, "s2": {"definition": "random(1,-1)", "group": "Ungrouped variables", "templateType": "anything", "description": "", "name": "s2"}, "b": {"definition": "s2*random(2..9)", "group": "Ungrouped variables", "templateType": "anything", "description": "", "name": "b"}, "s4": {"definition": "random(1,-1)", "group": "Ungrouped variables", "templateType": "anything", "description": "", "name": "s4"}, "f": {"definition": "random(2..9)", "group": "Ungrouped variables", "templateType": "anything", "description": "", "name": "f"}, "s1": {"definition": "random(1,-1)", "group": "Ungrouped variables", "templateType": "anything", "description": "", "name": "s1"}, "s3": {"definition": "random(1,-1)", "group": "Ungrouped variables", "templateType": "anything", "description": "", "name": "s3"}, "g": {"definition": "s1*random(2..9)", "group": "Ungrouped variables", "templateType": "anything", "description": "", "name": "g"}}, "advice": "<p>To find&nbsp;$\\boldsymbol{a\\times b}$ we take the determinant of the 3 by 3 matrix with first row = $(\\boldsymbol{i,j,k})$, second row = $\\boldsymbol{a}$ and third row = $\\boldsymbol{b}$</p>\n<p></p>\n<p>Hence:</p>\n<p></p>\n<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; \\begin{vmatrix} \\var{b} &amp; \\var{g} \\\\ \\var{d} &amp; \\var{f} \\end{vmatrix}\\boldsymbol{i}-\\begin{vmatrix} \\var{a} &amp; \\var{g} \\\\ \\var{c} &amp; \\var{f} \\end{vmatrix}\\boldsymbol{j}+\\begin{vmatrix} \\var{a} &amp; \\var{b} \\\\ \\var{c} &amp; \\var{d} \\end{vmatrix}\\boldsymbol{k} \\\\ \\\\ &amp;=&amp;\\simplify[]{({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>", "type": "question", "contributors": [{"name": "Julie Crowley", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/113/"}, {"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": "Simon Thomas", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3148/"}]}