// Numbas version: exam_results_page_options
{"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": [{"metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": "<p>Given vectors $\\boldsymbol{v}$ and $\\boldsymbol{w}$, find their inner product.</p>"}, "ungrouped_variables": ["a", "c", "b", "d", "g", "f", "s3", "s2", "s1", "s5", "s4", "inner"], "variablesTest": {"maxRuns": 100, "condition": ""}, "functions": {}, "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>", "extensions": [], "parts": [{"prompt": "<p>Find $\\boldsymbol{v&nbsp;\\cdot&nbsp;w} = $&nbsp;[[0]]</p>", "variableReplacements": [], "showFeedbackIcon": true, "type": "gapfill", "gaps": [{"variableReplacements": [], "showFeedbackIcon": false, "type": "jme", "vsetrangepoints": 5, "checkingtype": "absdiff", "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "expectedvariablenames": [], "marks": 2, "checkingaccuracy": 0.001, "checkvariablenames": false, "vsetrange": [0, 1], "scripts": {}, "answer": "{a}*{c}+{b}*{d}+{f}*{g}", "showpreview": true}], "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "marks": 0, "scripts": {}}], "rulesets": {"std": ["all", "fractionNumbers", "!collectNumbers", "!noLeadingMinus"]}, "preamble": {"css": "", "js": ""}, "name": "Vectors 4 (dot product)", "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>", "tags": [], "variable_groups": [], "variables": {"inner": {"name": "inner", "group": "Ungrouped variables", "templateType": "anything", "definition": "{a*c+b*d+f*g}", "description": ""}, "a": {"name": "a", "group": "Ungrouped variables", "templateType": "anything", "definition": "s1*random(2..9)", "description": ""}, "d": {"name": "d", "group": "Ungrouped variables", "templateType": "anything", "definition": "s4*random(2..9)", "description": ""}, "f": {"name": "f", "group": "Ungrouped variables", "templateType": "anything", "definition": "random(2..9)", "description": ""}, "b": {"name": "b", "group": "Ungrouped variables", "templateType": "anything", "definition": "s2*random(2..9)", "description": ""}, "g": {"name": "g", "group": "Ungrouped variables", "templateType": "anything", "definition": "s1*random(2..9)", "description": ""}, "s1": {"name": "s1", "group": "Ungrouped variables", "templateType": "anything", "definition": "random(1,-1)", "description": ""}, "s2": {"name": "s2", "group": "Ungrouped variables", "templateType": "anything", "definition": "random(1,-1)", "description": ""}, "s3": {"name": "s3", "group": "Ungrouped variables", "templateType": "anything", "definition": "random(1,-1)", "description": ""}, "s4": {"name": "s4", "group": "Ungrouped variables", "templateType": "anything", "definition": "random(1,-1)", "description": ""}, "s5": {"name": "s5", "group": "Ungrouped variables", "templateType": "anything", "definition": "random(1,-1)", "description": ""}, "c": {"name": "c", "group": "Ungrouped variables", "templateType": "anything", "definition": "s3*random(2..9)", "description": ""}}, "type": "question", "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/"}]}