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{"name": "Vectors: Perpendicular vectors", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"variablesTest": {"condition": "", "maxRuns": 100}, "extensions": [], "parts": [{"marks": 0, "gaps": [{"marks": "3", "maxValue": "x", "correctAnswerStyle": "plain", "scripts": {}, "showCorrectAnswer": true, "variableReplacements": [], "mustBeReduced": false, "correctAnswerFraction": true, "extendBaseMarkingAlgorithm": true, "unitTests": [], "allowFractions": true, "mustBeReducedPC": 0, "minValue": "x", "type": "numberentry", "notationStyles": ["plain", "en", "si-en"], "customMarkingAlgorithm": "", "showFeedbackIcon": true, "variableReplacementStrategy": "originalfirst"}], "scripts": {}, "showCorrectAnswer": true, "variableReplacements": [], "extendBaseMarkingAlgorithm": true, "sortAnswers": false, "unitTests": [], "type": "gapfill", "prompt": "<p>$\\boldsymbol{v} = \\begin{pmatrix}\\var{a} \\\\ \\var{b} \\\\ x \\end{pmatrix}$ and $\\boldsymbol{w} = \\begin{pmatrix} \\var{c} \\\\ \\var{d} \\\\ \\var{f} \\end{pmatrix}$.</p>\n<p>$\\boldsymbol{v}$ and $\\boldsymbol{w}$ are perpendicular.&nbsp; Determine $x$</p>\n<p>$x = $&nbsp;[[0]]</p>", "customMarkingAlgorithm": "", "showFeedbackIcon": true, "variableReplacementStrategy": "originalfirst"}], "name": "Vectors: Perpendicular vectors", "statement": "", "functions": {}, "ungrouped_variables": ["a", "b", "c", "d", "f", "s", "x", "v", "w"], "variables": {"v": {"definition": "vector(a,b,x)", "description": "", "group": "Ungrouped variables", "templateType": "anything", "name": "v"}, "a": {"definition": "s[0]*random(2..9)", "description": "", "group": "Ungrouped variables", "templateType": "anything", "name": "a"}, "x": {"definition": "(-a*c-b*d)/f", "description": "", "group": "Ungrouped variables", "templateType": "anything", "name": "x"}, "s": {"definition": "shuffle([1,1,1,-1,-1])", "description": "", "group": "Ungrouped variables", "templateType": "anything", "name": "s"}, "b": {"definition": "s[1]*random(2..9)", "description": "", "group": "Ungrouped variables", "templateType": "anything", "name": "b"}, "f": {"definition": "random(2,4,5,10)", "description": "", "group": "Ungrouped variables", "templateType": "anything", "name": "f"}, "c": {"definition": "s[2]*random(2..9)", "description": "", "group": "Ungrouped variables", "templateType": "anything", "name": "c"}, "d": {"definition": "s[3]*random(2..9)", "description": "", "group": "Ungrouped variables", "templateType": "anything", "name": "d"}, "w": {"definition": "vector(c,d,f)", "description": "", "group": "Ungrouped variables", "templateType": "anything", "name": "w"}}, "advice": "<p>See 16.4 and 16.5 for background and examples.&nbsp; Hint: the dot product is needed.</p>", "tags": [], "metadata": {"description": "<p>Two column vectors are given, with one entry unknown. Given that the vectors are perpendicular, question is to determine the unknown entry.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "preamble": {"js": "", "css": ""}, "rulesets": {"std": ["all", "fractionNumbers", "!collectNumbers", "!noLeadingMinus"]}, "variable_groups": [], "type": "question", "contributors": [{"name": "Lovkush Agarwal", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1358/"}]}]}], "contributors": [{"name": "Lovkush Agarwal", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1358/"}]}