// Numbas version: exam_results_page_options {"name": "MATH6005 Assessment 2_Q4of6", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"ungrouped_variables": ["a", "b", "c", "d", "f", "g", "result", "s1", "s2", "s3", "s4", "s5"], "rulesets": {"std": ["all", "fractionNumbers", "!collectNumbers", "!noLeadingMinus"]}, "variables": {"c": {"definition": "s3*random(2..9)", "group": "Ungrouped variables", "templateType": "anything", "description": "", "name": "c"}, "a": {"definition": "s1*random(2..9)", "group": "Ungrouped variables", "templateType": "anything", "description": "", "name": "a"}, "b": {"definition": "s2*random(2..9)", "group": "Ungrouped variables", "templateType": "anything", "description": "", "name": "b"}, "f": {"definition": "random(2..9)", "group": "Ungrouped variables", "templateType": "anything", "description": "", "name": "f"}, "s1": {"definition": "random(1,-1)", "group": "Ungrouped variables", "templateType": "anything", "description": "", "name": "s1"}, "s3": {"definition": "random(1,-1)", "group": "Ungrouped variables", "templateType": "anything", "description": "", "name": "s3"}, "result": {"definition": "cross(vector(a,b,g),vector(c,d,f))", "group": "Ungrouped variables", "templateType": "anything", "description": "", "name": "result"}, "s2": {"definition": "random(1,-1)", "group": "Ungrouped variables", "templateType": "anything", "description": "", "name": "s2"}, "s5": {"definition": "random(1,-1)", "group": "Ungrouped variables", "templateType": "anything", "description": "", "name": "s5"}, "d": {"definition": "s4*random(2..9)", "group": "Ungrouped variables", "templateType": "anything", "description": "", "name": "d"}, "g": {"definition": "s1*random(2..9)", "group": "Ungrouped variables", "templateType": "anything", "description": "", "name": "g"}, "s4": {"definition": "random(1,-1)", "group": "Ungrouped variables", "templateType": "anything", "description": "", "name": "s4"}}, "functions": {}, "variable_groups": [], "variablesTest": {"condition": "", "maxRuns": 100}, "extensions": [], "metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": "

Given vectors $\\boldsymbol{A,\\;B}$, find $\\boldsymbol{A\\times B}$

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\\begin{align}
\\boldsymbol{v} \\times \\boldsymbol{w} &= \\begin{pmatrix} \\simplify[basic]{{b}*{f}-{g}*{d}} \\\\ \\simplify[basic]{{g}*{c}-{a}*{f}} \\\\ \\simplify[basic]{{a}*{d}-{b}*{c}}  \\end{pmatrix} \\\\[1em]
&= \\var{result}
\\end{align}

", "statement": "

You are given the vectors $\\boldsymbol{v} = \\var{vector(a,b,g)}$, $\\boldsymbol{w} = \\var{vector(c,d,f)}$.

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Find

\n

$\\boldsymbol{v} \\times \\boldsymbol{w} = $ [[0]]

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