// Numbas version: finer_feedback_settings
{"name": "Find the curl of a vector field", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"variable_groups": [], "parts": [{"gaps": [{"showCorrectAnswer": true, "checkingtype": "absdiff", "vsetrange": [0, 1], "showpreview": true, "expectedvariablenames": ["x", "y", "z"], "checkingaccuracy": 0.001, "type": "jme", "checkvariablenames": true, "vsetrangepoints": 5, "marks": 1, "scripts": {}, "answersimplification": "all", "answer": "{c1*p8}*x^{p7}*y^{p8-1}*z^{p9}-{b1*p6}*x^{p4}*y^{p5}*z^{p6-1}"}, {"showCorrectAnswer": true, "checkingtype": "absdiff", "vsetrange": [0, 1], "showpreview": true, "expectedvariablenames": ["x", "y", "z"], "checkingaccuracy": 0.001, "type": "jme", "checkvariablenames": true, "vsetrangepoints": 5, "marks": 1, "scripts": {}, "answersimplification": "all", "answer": "{a1*p3}*x^{p1}*y^{p2}*z^{p3-1}-{c1*p7}*x^{p7-1}*y^{p8}*z^{p9}"}, {"showCorrectAnswer": true, "checkingtype": "absdiff", "vsetrange": [0, 1], "showpreview": true, "expectedvariablenames": ["x", "y", "z"], "checkingaccuracy": 0.001, "type": "jme", "checkvariablenames": true, "vsetrangepoints": 5, "marks": 1, "scripts": {}, "answersimplification": "all", "answer": "{b1*p4}*x^{p4-1}*y^{p5}*z^{p6}-{a1*p2}*x^{p1}*y^{p2-1}*z^{p3}"}], "showCorrectAnswer": true, "marks": 0, "prompt": "<p>$\\boldsymbol{\\nabla}\\times\\boldsymbol{u}=($[[0]]$,$[[1]]$,$[[2]]$)$.</p>", "scripts": {}, "type": "gapfill"}], "rulesets": {}, "variables": {"p9": {"definition": "random(0..4)", "templateType": "anything", "group": "Ungrouped variables", "name": "p9", "description": ""}, "p5": {"definition": "random(0..4)", "templateType": "anything", "group": "Ungrouped variables", "name": "p5", "description": ""}, "a1": {"definition": "random(2..9)*sign(random(-1,1))", "templateType": "anything", "group": "Ungrouped variables", "name": "a1", "description": ""}, "p8": {"definition": "random(0..4 except p2)", "templateType": "anything", "group": "Ungrouped variables", "name": "p8", "description": ""}, "b1": {"definition": "random(2..9)*sign(random(-1,1))", "templateType": "anything", "group": "Ungrouped variables", "name": "b1", "description": ""}, "p1": {"definition": "random(0..4)", "templateType": "anything", "group": "Ungrouped variables", "name": "p1", "description": ""}, "p2": {"definition": "random(0..4)", "templateType": "anything", "group": "Ungrouped variables", "name": "p2", "description": ""}, "p3": {"definition": "random(0..4)", "templateType": "anything", "group": "Ungrouped variables", "name": "p3", "description": ""}, "p4": {"definition": "random(0..4)", "templateType": "anything", "group": "Ungrouped variables", "name": "p4", "description": ""}, "c1": {"definition": "random(2..9)*sign(random(-1,1))", "templateType": "anything", "group": "Ungrouped variables", "name": "c1", "description": ""}, "p7": {"definition": "random(0..4 except p4)", "templateType": "anything", "group": "Ungrouped variables", "name": "p7", "description": ""}, "p6": {"definition": "random(0..4 except p3)", "templateType": "anything", "group": "Ungrouped variables", "name": "p6", "description": ""}}, "showQuestionGroupNames": false, "metadata": {"licence": "Creative Commons Attribution 4.0 International", "notes": "", "description": "<p>Curl of a vector field.</p>"}, "question_groups": [{"pickQuestions": 0, "pickingStrategy": "all-ordered", "name": "", "questions": []}], "type": "question", "preamble": {"js": "", "css": ""}, "tags": ["checked2015", "MAS2104"], "functions": {}, "name": "Find the curl of a vector field", "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["p2", "p3", "p1", "p6", "p7", "p4", "p5", "p8", "p9", "a1", "b1", "c1"], "statement": "<p>Find the curl $\\boldsymbol{\\nabla}\\times\\boldsymbol{u}$ of the vector field $\\boldsymbol{u}=\\pmatrix{\\simplify{{a1}*x^{p1}*y^{p2}*z^{p3}},\\simplify{{b1}*x^{p4}*y^{p5}*z^{p6}},\\simplify{{c1}*x^{p7}*y^{p8}*z^{p9}}}$.</p>", "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>", "contributors": [{"name": "Michael Proudman", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/269/"}]}]}], "contributors": [{"name": "Michael Proudman", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/269/"}]}