// Numbas version: exam_results_page_options
{"name": "Adding and subtracting vectors", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Adding and subtracting vectors", "tags": [], "metadata": {"description": "<p>Adding and subtracting vectors of random size, including resolving brackets. Advice (i.e. solution) has conditional visibility to show only the correct size.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "<p>Let \\(u=\\var{u}\\), \\(v=\\var{v}\\) and \\(w=\\var{w}\\).</p>", "advice": "<p>We add and subtract vectors entry by entry.</p>\n<p><strong>Part a)</strong></p>\n<p><span data-jme-visible=\"rows=2\">\\[\\simplify[unitFactor]{v+{sign1}w}=\\begin{pmatrix}\\simplify[]{{v[0]}+{sign1*w[0]}} \\\\ \\simplify[]{{v[1]}+{sign1*w[1]}}&nbsp; \\end{pmatrix} = \\var{v+sign1*w}\\]</span></p>\n<p><span data-jme-visible=\"rows=3\">\\[\\simplify[unitFactor]{v+{sign1}w}=\\begin{pmatrix}\\simplify[]{{v[0]}+{sign1*w[0]}} \\\\ \\simplify[]{{v[1]}+{sign1*w[1]}} \\\\\\simplify[]{{v[2]}+{sign1*w[2]}}&nbsp; \\end{pmatrix} = \\var{v+sign1*w}\\]</span></p>\n<p><span data-jme-visible=\"rows=4\">\\[\\simplify[unitFactor]{v+{sign1}w}=\\begin{pmatrix}\\simplify[]{{v[0]}+{sign1*w[0]}} \\\\ \\simplify[]{{v[1]}+{sign1*w[1]}} \\\\\\simplify[]{{v[2]}+{sign1*w[2]}} \\\\\\simplify[]{{v[3]}+{sign1*w[3]}} \\end{pmatrix} = \\var{v+sign1*w}\\] <br/></span></p>\n<p><strong>Part b)</strong></p>\n<p><span data-jme-visible=\"rows=2\">\\[v -(\\simplify[unitFactor,!expandBrackets]{u+{sign2}*w})=\\begin{pmatrix}\\simplify[]{{v[0]}-({u[0]}+{sign2*w[0]})} \\\\ \\simplify[]{{v[1]}-({u[1]}+{sign2*w[1]})} \\end{pmatrix}=\\var{v-(u+sign2*w)} \\]</span></p>\n<p><span data-jme-visible=\"rows=3\">\\[v -(\\simplify[unitFactor,!expandBrackets]{u+{sign2}*w})=\\begin{pmatrix}\\simplify[]{{v[0]}-({u[0]}+{sign2*w[0]})} \\\\ \\simplify[]{{v[1]}-({u[1]}+{sign2*w[1]})} \\\\\\simplify[]{{v[2]}-({u[2]}+{sign2*w[2]})} \\end{pmatrix}=\\var{v-(u+sign2*w)} \\]</span></p>\n<p><span data-jme-visible=\"rows=4\">\\[v -(\\simplify[unitFactor,!expandBrackets]{u+{sign2}*w})=\\begin{pmatrix}\\simplify[]{{v[0]}-({u[0]}+{sign2*w[0]})} \\\\ \\simplify[]{{v[1]}-({u[1]}+{sign2*w[1]})} \\\\\\simplify[]{{v[2]}-({u[2]}+{sign2*w[2]})} \\\\\\simplify[]{{v[3]}-({u[3]}+{sign2*w[3]})} \\end{pmatrix}=\\var{v-(u+sign2*w)} \\]</span></p>", "rulesets": {}, "extensions": [], "variables": {"rows": {"name": "rows", "group": "Ungrouped variables", "definition": "random(2..4)", "description": "<p>size of the vectors</p>", "templateType": "anything"}, "v": {"name": "v", "group": "Ungrouped variables", "definition": "vector((repeat(random(-5..5),rows)))", "description": "<p>randomly generated vector of random size.</p>", "templateType": "anything"}, "w": {"name": "w", "group": "Ungrouped variables", "definition": "vector(repeat(random(-5..5),rows))", "description": "<p>randomly generated vector of same size as v</p>", "templateType": "anything"}, "u": {"name": "u", "group": "Ungrouped variables", "definition": "vector(repeat(random(-5..5),rows))", "description": "<p>randomly generated vector of same size as v</p>", "templateType": "anything"}, "sign1": {"name": "sign1", "group": "Ungrouped variables", "definition": "random(-1..1 except 0)", "description": "<p>randomly generated sign</p>", "templateType": "anything"}, "sign2": {"name": "sign2", "group": "Ungrouped variables", "definition": "random(-1..1 except 0)", "description": "", "templateType": "anything"}}, "variablesTest": {"condition": "not is_zero(v) and not is_zero(w) and not is_zero(u)", "maxRuns": 100}, "ungrouped_variables": ["rows", "v", "w", "u", "sign1", "sign2"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Calculate \\(\\simplify{v + {sign1}*w}=\\) [[0]].</p>\n<p></p>", "gaps": [{"type": "matrix", "useCustomName": true, "customName": "Gap 0", "marks": "2", "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "correctAnswer": "v+sign1*w", "correctAnswerFractions": false, "numRows": "1", "numColumns": "1", "allowResize": true, "tolerance": 0, "markPerCell": true, "allowFractions": false, "minColumns": 1, "maxColumns": "1", "minRows": 1, "maxRows": 0}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, 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"contributors": [{"name": "Tatiana Tyukina", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/341/"}, {"name": "Julia Goedecke", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/5121/"}]}]}], "contributors": [{"name": "Tatiana Tyukina", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/341/"}, {"name": "Julia Goedecke", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/5121/"}]}