// Numbas version: finer_feedback_settings
{"name": "Violeta's copy of Vectors 4 (dot product)", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"variable_groups": [], "tags": [], "variables": {"s2": {"group": "Ungrouped variables", "definition": "random(1,-1)", "name": "s2", "description": "", "templateType": "anything"}, "s4": {"group": "Ungrouped variables", "definition": "random(1,-1)", "name": "s4", "description": "", "templateType": "anything"}, "s1": {"group": "Ungrouped variables", "definition": "random(1,-1)", "name": "s1", "description": "", "templateType": "anything"}, "b": {"group": "Ungrouped variables", "definition": "s2*random(2..9)", "name": "b", "description": "", "templateType": "anything"}, "a": {"group": "Ungrouped variables", "definition": "s1*random(2..9)", "name": "a", "description": "", "templateType": "anything"}, "inner": {"group": "Ungrouped variables", "definition": "{a*c+b*d+f*g}", "name": "inner", "description": "", "templateType": "anything"}, "d": {"group": "Ungrouped variables", "definition": "s4*random(2..9)", "name": "d", "description": "", "templateType": "anything"}, "s3": {"group": "Ungrouped variables", "definition": "random(1,-1)", "name": "s3", "description": "", "templateType": "anything"}, "c": {"group": "Ungrouped variables", "definition": "s3*random(2..9)", "name": "c", "description": "", "templateType": "anything"}, "s5": {"group": "Ungrouped variables", "definition": "random(1,-1)", "name": "s5", "description": "", "templateType": "anything"}, "g": {"group": "Ungrouped variables", "definition": "s1*random(2..9)", "name": "g", "description": "", "templateType": "anything"}, "f": {"group": "Ungrouped variables", "definition": "random(2..9)", "name": "f", "description": "", "templateType": "anything"}}, "extensions": [], "preamble": {"css": "", "js": ""}, "functions": {}, "variablesTest": {"condition": "", "maxRuns": 100}, "parts": [{"showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "marks": 0, "scripts": {}, "prompt": "<p>Find $\\boldsymbol{v&nbsp;\\cdot&nbsp;w} = $&nbsp;[[0]]</p>", "type": "gapfill", "variableReplacementStrategy": "originalfirst", "gaps": [{"correctAnswerFraction": false, "type": "numberentry", "mustBeReducedPC": 0, "marks": 2, "correctAnswerStyle": "plain", "mustBeReduced": false, "showFeedbackIcon": true, "maxValue": "a*c+b*d+f*g", "minValue": "a*c+b*d+f*g", "showCorrectAnswer": true, "allowFractions": true, "variableReplacements": [], "scripts": {}, "notationStyles": ["plain", "en", "si-en"], "variableReplacementStrategy": "originalfirst"}]}], "rulesets": {"std": ["all", "fractionNumbers", "!collectNumbers", "!noLeadingMinus"]}, "metadata": {"description": "<p>Given vectors $\\boldsymbol{v}$ and $\\boldsymbol{w}$, find their inner product.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "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": "Violeta's copy of 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>", "ungrouped_variables": ["a", "c", "b", "d", "g", "f", "s3", "s2", "s1", "s5", "s4", "inner"], "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/"}]}