// Numbas version: exam_results_page_options
{"name": "Angle between two vectors (3D)", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"variables": {"s2": {"group": "Ungrouped variables", "description": "", "templateType": "anything", "definition": "random(1,-1)", "name": "s2"}, "c": {"group": "Ungrouped variables", "description": "", "templateType": "anything", "definition": "s3*random(2..9)", "name": "c"}, "d": {"group": "Ungrouped variables", "description": "", "templateType": "anything", "definition": "s4*random(2..9)", "name": "d"}, "k1": {"group": "Ungrouped variables", "description": "", "templateType": "anything", "definition": "random(2..5)", "name": "k1"}, "k2": {"group": "Ungrouped variables", "description": "", "templateType": "anything", "definition": "random(2..5)", "name": "k2"}, "b": {"group": "Ungrouped variables", "description": "", "templateType": "anything", "definition": "s2*random(2..9)", "name": "b"}, "g": {"group": "Ungrouped variables", "description": "", "templateType": "anything", "definition": "s1*random(2..9)", "name": "g"}, "s4": {"group": "Ungrouped variables", "description": "", "templateType": "anything", "definition": "random(1,-1)", "name": "s4"}, "s3": {"group": "Ungrouped variables", "description": "", "templateType": "anything", "definition": "random(1,-1)", "name": "s3"}, "s5": {"group": "Ungrouped variables", "description": "", "templateType": "anything", "definition": "random(1,-1)", "name": "s5"}, "s1": {"group": "Ungrouped variables", "description": "", "templateType": "anything", "definition": "random(1,-1)", "name": "s1"}, "f": {"group": "Ungrouped variables", "description": "", "templateType": "anything", "definition": "random(2..9)", "name": "f"}, "lena": {"group": "Ungrouped variables", "description": "", "templateType": "anything", "definition": "length(vector(a,b,c))", "name": "lena"}, "a": {"group": "Ungrouped variables", "description": "", "templateType": "anything", "definition": "s1*random(2..9)", "name": "a"}}, "extensions": [], "variable_groups": [], "advice": "", "metadata": {"description": "", "licence": "Creative Commons Attribution 4.0 International"}, "rulesets": {"std": ["all", "fractionNumbers", "!collectNumbers", "!noLeadingMinus"]}, "functions": {}, "tags": [], "name": "Angle between two vectors (3D)", "preamble": {"css": "", "js": ""}, "parts": [{"type": "gapfill", "scripts": {}, "showCorrectAnswer": true, "prompt": "<p>Given that the angle between these two vectors is $\\theta$ find the <strong>exact</strong> value of $\\cos \\theta$.</p>\n<p>$\\cos \\theta = $</p>", "marks": 0, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true}, {"type": "gapfill", "scripts": {}, "showCorrectAnswer": true, "prompt": "<p>Find&nbsp;$\\var{k1}\\boldsymbol{a} - \\var{k2}\\boldsymbol{b} = $&nbsp;[[0]]</p>", "marks": 0, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"showCorrectAnswer": true, "numRows": "3", "variableReplacements": [], "correctAnswerFractions": false, "allowResize": false, "variableReplacementStrategy": "originalfirst", "allowFractions": false, "type": "matrix", "scripts": {}, "numColumns": 1, "markPerCell": false, "tolerance": 0, "correctAnswer": "{result3}", "marks": "2", "showFeedbackIcon": true}], "showFeedbackIcon": true}, {"type": "gapfill", "scripts": {}, "showCorrectAnswer": true, "prompt": "<p>Find&nbsp;$\\boldsymbol{a}\\cdot\\boldsymbol{b} = $&nbsp;[[0]]</p>", "marks": 0, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"maxValue": "{result2}", "correctAnswerFraction": false, "mustBeReducedPC": 0, "marks": "2", "variableReplacements": [], "showCorrectAnswer": true, "mustBeReduced": false, "allowFractions": false, "type": "numberentry", "scripts": {}, "minValue": "{result2}", "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain", "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true}], "showFeedbackIcon": true}], "statement": "<p>Consider&nbsp;the vectors $\\boldsymbol{a} = \\var{vector(a,b,c)}$, $\\boldsymbol{b} = \\var{vector(d,f,g)}$.</p>", "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["a", "b", "c", "d", "f", "g", "s1", "s2", "s3", "s4", "s5", "k1", "k2", "lena"], "type": "question", "contributors": [{"name": "Adrian Jannetta", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/164/"}]}]}], "contributors": [{"name": "Adrian Jannetta", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/164/"}]}