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{"name": "Dot and cross product combinations", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"variable_groups": [], "variables": {}, "ungrouped_variables": [], "question_groups": [{"pickingStrategy": "all-ordered", "questions": [], "name": "", "pickQuestions": 0}], "name": "Dot and cross product combinations", "showQuestionGroupNames": false, "functions": {}, "parts": [{"displayType": "radiogroup", "layout": {"type": "all", "expression": ""}, "choices": ["<p>$\\boldsymbol{(A\\cdot B)\\cdot C}$</p>", "<p>$\\boldsymbol{(A\\cdot B)C}$</p>", "<p>$\\boldsymbol{(A\\cdot B)\\times C}$</p>", "<p>$\\boldsymbol{(A\\times B)\\times C}$</p>", "<p>$\\boldsymbol{(A\\times B)\\cdot C}$</p>"], "showCorrectAnswer": true, "matrix": [[0, 0, 0.4], [0, 0.4, 0], [0, 0, 0.4], [0, 0.4, 0], [0.4, 0, 0]], "minAnswers": 0, "maxAnswers": 0, "shuffleChoices": true, "marks": 0, "scripts": {}, "maxMarks": 0, "type": "m_n_x", "minMarks": 0, "shuffleAnswers": true, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "answers": ["<p>Scalar</p>", "<p>Vector</p>", "<p>Undefined</p>"], "warningType": "none"}], "variablesTest": {"condition": "", "maxRuns": 100}, "statement": "<p>Given the vectors $\\boldsymbol{A},\\;\\;\\boldsymbol{B}$ and $\\boldsymbol{C}$ in $3$ dimensional space, state whether the following quantities are scalars, vectors or undefined.</p>", "tags": ["checked2015", "cross product", "dot product", "inner product", "mas1602", "MAS2104", "scalar product", "scalars", "unused", "vector", "Vector", "vector product", "vectors"], "rulesets": {"std": ["all", "fractionNumbers", "!collectNumbers", "!noLeadingMinus"]}, "preamble": {"css": "", "js": ""}, "type": "question", "metadata": {"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><strong>Added tags.<br /></strong></p>\n        \t\t<p><strong>&nbsp;</strong></p>\n        \t\t<p><strong>&nbsp;</strong></p>\n        \t\t", "licence": "Creative Commons Attribution 4.0 International", "description": "<p>Determine if various combinations of vectors are defined or not.</p>"}, "advice": "\n  \n  \n  <p>1. $\\boldsymbol{(A\\cdot B)\\cdot C}$ is <b>undefined</b> as $\\boldsymbol{A\\cdot B}$ is a scalar and we cannot take the inner product of a scalar with the vector $\\boldsymbol{C}$.</p>\n  \n  \n  \n  <p>2. $\\boldsymbol{(A\\cdot B)C}$ is a <b>vector</b> and is a multiple of $\\boldsymbol{C}$ as $\\boldsymbol{A \\cdot B}$ is a scalar.</p>\n  \n  \n  \n  <p>3. $\\boldsymbol{(A\\cdot B)\\times C}$ is <b>undefined</b> as $\\boldsymbol{A\\cdot B}$ is a scalar and the cross product is only defined between vectors.</p>\n  \n  \n  \n  <p>4. $\\boldsymbol{(A\\times B)\\times C}$ is a <b>vector</b> as $\\boldsymbol{A \\times B}$ and $\\boldsymbol{C}$ are vectors and the cross product between vectors produces a vector.</p>\n  \n  \n  \n  <p>5. $\\boldsymbol{(A\\times B)\\cdot C}$ is a <b>scalar</b> as $\\boldsymbol{A \\times B}$ and $\\boldsymbol{C}$ are vectors and the inner or dot product is between vectors and produces a scalar.</p>\n  \n  \n    ", "contributors": [{"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/697/"}]}]}], "contributors": [{"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/697/"}]}