// Numbas version: exam_results_page_options
{"name": "Inner product of two vectors", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"parts": [{"variableReplacementStrategy": "originalfirst", "scripts": {}, "gaps": [{"showCorrectAnswer": true, "showPrecisionHint": false, "variableReplacementStrategy": "originalfirst", "allowFractions": false, "scripts": {}, "type": "numberentry", "correctAnswerFraction": false, "minValue": "{inner}", "maxValue": "{inner}", "variableReplacements": [], "marks": 2}], "type": "gapfill", "showCorrectAnswer": true, "prompt": "<p>Find $\\boldsymbol{v&nbsp;\\cdot&nbsp;w} = $&nbsp;[[0]]</p>", "variableReplacements": [], "marks": 0}], "variables": {"s1": {"group": "Ungrouped variables", "templateType": "anything", "definition": "random(1,-1)", "name": "s1", "description": ""}, "s5": {"group": "Ungrouped variables", "templateType": "anything", "definition": "random(1,-1)", "name": "s5", "description": ""}, "b": {"group": "Ungrouped variables", "templateType": "anything", "definition": "s2*random(2..9)", "name": "b", "description": ""}, "c": {"group": "Ungrouped variables", "templateType": "anything", "definition": "s3*random(2..9)", "name": "c", "description": ""}, "f": {"group": "Ungrouped variables", "templateType": "anything", "definition": "random(2..9)", "name": "f", "description": ""}, "s4": {"group": "Ungrouped variables", "templateType": "anything", "definition": "random(1,-1)", "name": "s4", "description": ""}, "s2": {"group": "Ungrouped variables", "templateType": "anything", "definition": "random(1,-1)", "name": "s2", "description": ""}, "inner": {"group": "Ungrouped variables", "templateType": "anything", "definition": "{a*c+b*d+f*g}", "name": "inner", "description": ""}, "s3": {"group": "Ungrouped variables", "templateType": "anything", "definition": "random(1,-1)", "name": "s3", "description": ""}, "a": {"group": "Ungrouped variables", "templateType": "anything", "definition": "s1*random(2..9)", "name": "a", "description": ""}, "d": {"group": "Ungrouped variables", "templateType": "anything", "definition": "s4*random(2..9)", "name": "d", "description": ""}, "g": {"group": "Ungrouped variables", "templateType": "anything", "definition": "s1*random(2..9)", "name": "g", "description": ""}}, "ungrouped_variables": ["a", "c", "b", "d", "g", "f", "s3", "s2", "s1", "s5", "s4", "inner"], "question_groups": [{"pickingStrategy": "all-ordered", "questions": [], "name": "", "pickQuestions": 0}], "name": "Inner product of two vectors", "showQuestionGroupNames": false, "variable_groups": [], "functions": {}, "variablesTest": {"condition": "", "maxRuns": 100}, "statement": "<p>You are given the vectors $\\boldsymbol{v}= \\var{vector(a,b,g)}$ and $\\boldsymbol{w} = \\var{vector(c,d,f)}$ in $\\mathbb{R}^3$.</p>", "tags": ["checked2015", "dot product", "dot product of two vectors", "inner product", "mas1602", "MAS1602", "scalar product", "three dimensional vectors", "unused", "vectors"], "rulesets": {"std": ["all", "fractionNumbers", "!collectNumbers", "!noLeadingMinus"]}, "preamble": {"css": "", "js": ""}, "type": "question", "metadata": {"notes": "\n            \t\t<p><strong>15/07/2012:</strong></p>\n            \t\t<p>Added tags.</p>\n            \t\t<p><strong>16/07/2012:</strong></p>\n            \t\t<p>Added tags.<strong><br /></strong></p>\n            \t\t<p>Question appears to be working correctly.</p>\n            \t\t", "licence": "Creative Commons Attribution 4.0 International", "description": "<p>Given vectors $\\boldsymbol{v}$ and $\\boldsymbol{w}$, find their inner product.</p>"}, "advice": "<p>\\begin{align}<br/>\\boldsymbol{v \\cdot w} &amp;= \\var{vector(a,b,g)} \\boldsymbol{\\cdot} \\var{vector(c,d,f)} \\\\<br/>&amp;= \\simplify[]{{a}*{c}+{b}*{d}+{g}*{f}} \\\\<br/> &amp;= \\var{inner}<br/>\\end{align}</p>", "contributors": [{"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/697/"}]}]}], "contributors": [{"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/697/"}]}