// Numbas version: exam_results_page_options
{"name": "ZTest_Belinda's copy of Harry's copy of 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": [{"preamble": {"css": "", "js": ""}, "parts": [{"unitTests": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"failureRate": 1, "vsetRangePoints": 5, "unitTests": [], "variableReplacementStrategy": "originalfirst", "showPreview": true, "answer": "{c1*p8}*x^{p7}*y^{p8-1}*z^{p9}-{b1*p6}*x^{p4}*y^{p5}*z^{p6-1}", "checkingAccuracy": 0.001, "customMarkingAlgorithm": "", "marks": 1, "type": "jme", "showFeedbackIcon": true, "answerSimplification": "all", "checkingType": "absdiff", "checkVariableNames": true, "extendBaseMarkingAlgorithm": true, "scripts": {}, "vsetRange": [0, 1], "showCorrectAnswer": true, "expectedVariableNames": ["x", "y", "z"], "variableReplacements": []}, {"failureRate": 1, "vsetRangePoints": 5, "unitTests": [], "variableReplacementStrategy": "originalfirst", "showPreview": true, "answer": "{a1*p3}*x^{p1}*y^{p2}*z^{p3-1}-{c1*p7}*x^{p7-1}*y^{p8}*z^{p9}", "checkingAccuracy": 0.001, "customMarkingAlgorithm": "", "marks": 1, "type": "jme", "showFeedbackIcon": true, "answerSimplification": "all", "checkingType": "absdiff", "checkVariableNames": true, "extendBaseMarkingAlgorithm": true, "scripts": {}, "vsetRange": [0, 1], "showCorrectAnswer": true, "expectedVariableNames": ["x", "y", "z"], "variableReplacements": []}, {"failureRate": 1, "vsetRangePoints": 5, "unitTests": [], "variableReplacementStrategy": "originalfirst", "showPreview": true, "answer": "{b1*p4}*x^{p4-1}*y^{p5}*z^{p6}-{a1*p2}*x^{p1}*y^{p2-1}*z^{p3}", "checkingAccuracy": 0.001, "customMarkingAlgorithm": "", "marks": 1, "type": "jme", "showFeedbackIcon": true, "answerSimplification": "all", "checkingType": "absdiff", "checkVariableNames": true, "extendBaseMarkingAlgorithm": true, "scripts": {}, "vsetRange": [0, 1], "showCorrectAnswer": true, "expectedVariableNames": ["x", "y", "z"], "variableReplacements": []}], "customMarkingAlgorithm": "", "prompt": "<p>$\\boldsymbol{\\nabla}\\times\\boldsymbol{u}=$[[0]] $i$ + [[1]] $j$ + [[2]] $k$</p>", "marks": 0, "type": "gapfill", "sortAnswers": false, "showFeedbackIcon": true, "extendBaseMarkingAlgorithm": true, "scripts": {}, "showCorrectAnswer": true, "variableReplacements": []}], "name": "ZTest_Belinda's copy of Harry's copy of Find the curl of a vector field", "metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": "<p>Curl of a vector field.</p>"}, "variablesTest": {"maxRuns": 100, "condition": ""}, "ungrouped_variables": ["p2", "p3", "p1", "p6", "p7", "p4", "p5", "p8", "p9", "a1", "b1", "c1"], "extensions": [], "tags": [], "functions": {}, "rulesets": {}, "variables": {"p5": {"templateType": "anything", "description": "", "definition": "random(0..4)", "name": "p5", "group": "Ungrouped variables"}, "p7": {"templateType": "anything", "description": "", "definition": "random(0..4 except p4)", "name": "p7", "group": "Ungrouped variables"}, "a1": {"templateType": "anything", "description": "", "definition": "random(2..9)*sign(random(-1,1))", "name": "a1", "group": "Ungrouped variables"}, "p8": {"templateType": "anything", "description": "", "definition": "random(0..4 except p2)", "name": "p8", "group": "Ungrouped variables"}, "b1": {"templateType": "anything", "description": "", "definition": "random(2..9)*sign(random(-1,1))", "name": "b1", "group": "Ungrouped variables"}, "p9": {"templateType": "anything", "description": "", "definition": "random(0..4)", "name": "p9", "group": "Ungrouped variables"}, "p1": {"templateType": "anything", "description": "", "definition": "random(0..4)", "name": "p1", "group": "Ungrouped variables"}, "p3": {"templateType": "anything", "description": "", "definition": "random(0..4)", "name": "p3", "group": "Ungrouped variables"}, "c1": {"templateType": "anything", "description": "", "definition": "random(2..9)*sign(random(-1,1))", "name": "c1", "group": "Ungrouped variables"}, "p6": {"templateType": "anything", "description": "", "definition": "random(0..4 except p3)", "name": "p6", "group": "Ungrouped variables"}, "p2": {"templateType": "anything", "description": "", "definition": "random(0..4)", "name": "p2", "group": "Ungrouped variables"}, "p4": {"templateType": "anything", "description": "", "definition": "random(0..4)", "name": "p4", "group": "Ungrouped variables"}}, "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>", "variable_groups": [], "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>", "type": "question", "contributors": [{"name": "Belinda Schwerin", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2286/"}]}]}], "contributors": [{"name": "Belinda Schwerin", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2286/"}]}