// Numbas version: finer_feedback_settings
{"name": "Vectors 4 (dot product)", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"type": "question", "preamble": {"js": "", "css": ""}, "parts": [{"gaps": [{"type": "numberentry", "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "showPrecisionHint": false, "scripts": {}, "marks": 2, "allowFractions": false, "minValue": "{inner}", "correctAnswerFraction": false, "showCorrectAnswer": true, "maxValue": "{inner}"}], "type": "gapfill", "variableReplacements": [], "scripts": {}, "marks": 0, "prompt": "<p>Find $\\boldsymbol{v&nbsp;\\cdot&nbsp;w} = $&nbsp;[[0]]</p>", "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst"}], "metadata": {"description": "<p>Given vectors $\\boldsymbol{v}$ and $\\boldsymbol{w}$, find their inner product.</p>", "licence": "Creative Commons Attribution 4.0 International", "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"}, "tags": ["checked2015", "dot product", "dot product of two vectors", "inner product", "mas1602", "MAS1602", "scalar product", "three dimensional vectors", "unused", "vectors"], "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>", "rulesets": {"std": ["all", "fractionNumbers", "!collectNumbers", "!noLeadingMinus"]}, "variable_groups": [], "variables": {"b": {"definition": "s2*random(2..9)", "templateType": "anything", "description": "", "group": "Ungrouped variables", "name": "b"}, "d": {"definition": "s4*random(2..9)", "templateType": "anything", "description": "", "group": "Ungrouped variables", "name": "d"}, "inner": {"definition": "{a*c+b*d+f*g}", "templateType": "anything", "description": "", "group": "Ungrouped variables", "name": "inner"}, "g": {"definition": "s1*random(2..9)", "templateType": "anything", "description": "", "group": "Ungrouped variables", "name": "g"}, "c": {"definition": "s3*random(2..9)", "templateType": "anything", "description": "", "group": "Ungrouped variables", "name": "c"}, "s2": {"definition": "random(1,-1)", "templateType": "anything", "description": "", "group": "Ungrouped variables", "name": "s2"}, "s5": {"definition": "random(1,-1)", "templateType": "anything", "description": "", "group": "Ungrouped variables", "name": "s5"}, "s3": {"definition": "random(1,-1)", "templateType": "anything", "description": "", "group": "Ungrouped variables", "name": "s3"}, "s4": {"definition": "random(1,-1)", "templateType": "anything", "description": "", "group": "Ungrouped variables", "name": "s4"}, "f": {"definition": "random(2..9)", "templateType": "anything", "description": "", "group": "Ungrouped variables", "name": "f"}, "s1": {"definition": "random(1,-1)", "templateType": "anything", "description": "", "group": "Ungrouped variables", "name": "s1"}, "a": {"definition": "s1*random(2..9)", "templateType": "anything", "description": "", "group": "Ungrouped variables", "name": "a"}}, "showQuestionGroupNames": false, "ungrouped_variables": ["a", "c", "b", "d", "g", "f", "s3", "s2", "s1", "s5", "s4", "inner"], "variablesTest": {"maxRuns": 100, "condition": ""}, "question_groups": [{"pickQuestions": 0, "questions": [], "pickingStrategy": "all-ordered", "name": ""}], "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>", "name": "Vectors 4 (dot product)", "functions": {}, "contributors": [{"name": "Violeta CIT", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1030/"}]}]}], "contributors": [{"name": "Violeta CIT", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1030/"}]}