// Numbas version: finer_feedback_settings
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"random(2..9)*sign(random(-1,1))"}, "p8": {"name": "p8", "templateType": "anything", "description": "", "group": "Ungrouped variables", "definition": "random(0..4 except p2)"}, "p4": {"name": "p4", "templateType": "anything", "description": "", "group": "Ungrouped variables", "definition": "random(0..4)"}, "p6": {"name": "p6", "templateType": "anything", "description": "", "group": "Ungrouped variables", "definition": "random(0..4 except p3)"}, "p9": {"name": "p9", "templateType": "anything", "description": "", "group": "Ungrouped variables", "definition": "random(0..4)"}, "p5": {"name": "p5", "templateType": "anything", "description": "", "group": "Ungrouped variables", "definition": "random(0..4)"}, "b1": {"name": "b1", "templateType": "anything", "description": "", "group": "Ungrouped variables", "definition": "random(2..9)*sign(random(-1,1))"}, "p1": {"name": "p1", "templateType": "anything", "description": "", "group": "Ungrouped variables", "definition": "random(0..4)"}}, "metadata": {"description": "<p>Curl of a vector field.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "name": "Harry's copy of Find the curl of a vector field", "parts": [{"variableReplacements": [], "showCorrectAnswer": true, "type": "gapfill", "gaps": [{"variableReplacements": [], "checkingtype": "absdiff", "showCorrectAnswer": true, "type": "jme", "checkvariablenames": true, "expectedvariablenames": ["x", "y", "z"], "answer": "{c1*p8}*x^{p7}*y^{p8-1}*z^{p9}-{b1*p6}*x^{p4}*y^{p5}*z^{p6-1}", "showFeedbackIcon": true, "variableReplacementStrategy": "originalfirst", "showpreview": true, "answersimplification": "all", "vsetrangepoints": 5, "vsetrange": [0, 1], "checkingaccuracy": 0.001, "scripts": {}, "marks": 1}, {"variableReplacements": [], "checkingtype": "absdiff", "showCorrectAnswer": true, "type": "jme", "checkvariablenames": true, "expectedvariablenames": ["x", "y", "z"], "answer": "{a1*p3}*x^{p1}*y^{p2}*z^{p3-1}-{c1*p7}*x^{p7-1}*y^{p8}*z^{p9}", "showFeedbackIcon": true, "variableReplacementStrategy": "originalfirst", "showpreview": true, "answersimplification": "all", "vsetrangepoints": 5, "vsetrange": [0, 1], "checkingaccuracy": 0.001, "scripts": {}, "marks": 1}, {"variableReplacements": [], "checkingtype": "absdiff", "showCorrectAnswer": true, "type": "jme", "checkvariablenames": true, "expectedvariablenames": ["x", "y", "z"], "answer": "{b1*p4}*x^{p4-1}*y^{p5}*z^{p6}-{a1*p2}*x^{p1}*y^{p2-1}*z^{p3}", "showFeedbackIcon": true, "variableReplacementStrategy": "originalfirst", "showpreview": true, "answersimplification": "all", "vsetrangepoints": 5, "vsetrange": [0, 1], "checkingaccuracy": 0.001, "scripts": {}, "marks": 1}], "prompt": "<p>$\\boldsymbol{\\nabla}\\times\\boldsymbol{u}=$[[0]] $i$ + [[1]] $j$ + [[2]] $k$</p>", "showFeedbackIcon": true, "variableReplacementStrategy": "originalfirst", "scripts": {}, "marks": 0}], "rulesets": {}, "variable_groups": [], "variablesTest": {"condition": "", "maxRuns": 100}, "tags": [], "extensions": [], "statement": "<p>Find the curl $\\boldsymbol{\\nabla}\\times\\boldsymbol{u}$ of the vector field $\\boldsymbol{u}=(\\simplify{{a1}*x^{p1}*y^{p2}*z^{p3}})i + (\\simplify{{b1}*x^{p4}*y^{p5}*z^{p6}}) j + (\\simplify{{c1}*x^{p7}*y^{p8}*z^{p9}}) k$.</p>\n<p></p>\n<h6>Note on entering solution: For example: input $xyz$ as $x$*$y$*$z$</h6>", "preamble": {"css": "", "js": ""}, "ungrouped_variables": ["p2", "p3", "p1", "p6", "p7", "p4", "p5", "p8", "p9", "a1", "b1", "c1"], "advice": "<p>The curl of a vector field $\\boldsymbol{u}=\\pmatrix{u_x,u_y,u_z}$ is given by</p>\n  <p>\\[\\boldsymbol{\\nabla}\\times\\boldsymbol{u}=\\pmatrix{\\frac{\\partial u_z}{\\partial y}-\\frac{\\partial u_y}{\\partial z},\\frac{\\partial u_x}{\\partial z}-\\frac{\\partial u_z}{\\partial x},\\frac{\\partial u_y}{\\partial x}-\\frac{\\partial u_x}{\\partial y}}.\\]</p>\n  <p>Hence, in this example, after straight forward partial differentiation</p>\n  <p>\\[\\boldsymbol{\\nabla}\\times\\boldsymbol{u}=\\pmatrix{\\simplify{{c1*p8}*x^{p7}*y^{p8-1}*z^{p9}-{b1*p6}*x^{p4}*y^{p5}*z^{p6-1}},\\simplify{{a1*p3}*x^{p1}*y^{p2}*z^{p3-1}-{c1*p7}*x^{p7-1}*y^{p8}*z^{p9}},\\simplify{{b1*p4}*x^{p4-1}*y^{p5}*z^{p6}-{a1*p2}*x^{p1}*y^{p2-1}*z^{p3}}}.\\]</p>", "type": "question", "contributors": [{"name": "Harry Flynn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/976/"}]}]}], "contributors": [{"name": "Harry Flynn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/976/"}]}