// Numbas version: exam_results_page_options
{"name": "Calculate distance from a point to a plane", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"parts": [{"precisionPartialCredit": 0, "variableReplacementStrategy": "originalfirst", "maxValue": "abs(a*px+b*py+c*pz+d)/(sqrt(a^2+b^2+c^2))", "showCorrectAnswer": true, "precision": "2", "type": "numberentry", "scripts": {}, "correctAnswerStyle": "plain", "precisionMessage": "You have not given your answer to the correct precision.", "notationStyles": ["plain", "plain-eu"], "showFeedbackIcon": true, "minValue": "abs(a*px+b*py+c*pz+d)/(sqrt(a^2+b^2+c^2))", "precisionType": "sigfig", "marks": 1, "correctAnswerFraction": false, "showPrecisionHint": true, "strictPrecision": true, "variableReplacements": [], "prompt": "<p>$P(\\var{px},\\var{py},\\var{pz})$, $\\pi \\equiv \\simplify{{a}*x+{b}*y+{c}*z+{d}}=0$</p>", "allowFractions": false}], "rulesets": {}, "preamble": {"css": "", "js": ""}, "variables": {"b": {"description": "<p>B coefficient of the equation of plane $\\pi$.</p>", "definition": "random(-10..10#1)", "templateType": "randrange", "group": "Ungrouped variables", "name": "b"}, "d": {"description": "<p>Intercept term of the equation of plane $\\pi$.</p>", "definition": "random(-10..10#1)", "templateType": "randrange", "group": "Ungrouped variables", "name": "d"}, "pz": {"description": "<p>z coordinate of point P</p>", "definition": "random(-10..10#1)", "templateType": "randrange", "group": "Ungrouped variables", "name": "pz"}, "py": {"description": "<p>y coordinate of point P</p>", "definition": "random(-10..10#1)", "templateType": "randrange", "group": "Ungrouped variables", "name": "py"}, "c": {"description": "<p>C coefficient of the equation of plane $\\pi$.</p>", "definition": "random(-10..10#1)", "templateType": "randrange", "group": "Ungrouped variables", "name": "c"}, "a": {"description": "<p>A coefficient of the equation of the plane $\\pi$.</p>", "definition": "random(-10..10#1)", "templateType": "randrange", "group": "Ungrouped variables", "name": "a"}, "px": {"description": "<p>x coordinate of point P</p>", "definition": "random(-10..10#1)", "templateType": "randrange", "group": "Ungrouped variables", "name": "px"}}, "functions": {}, "variablesTest": {"condition": "", "maxRuns": 100}, "metadata": {"description": "<p>This question assesses the knowledge of the formula to calculate the distance between a point and a plane in the 3D space.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "tags": [], "extensions": [], "name": "Calculate distance from a point to a plane", "variable_groups": [], "advice": "<p>The distance from a point $P(p_x,p_y,p_z)$ to a plane $\\pi: Ax+By+Cz+D=0$ is given by:</p>\n<p>\\[ d(P,\\pi) = \\dfrac{|Ap_x+Bp_y+Cp_z+D|}{\\sqrt{A^2+B^2+C^2}} \\]</p>\n<p>To find the distance you might also find the orthogonal projection of $P$ on $\\pi$, and then calculate the distance between $P$ and its projection on $\\pi$. The orthogonal porjection is the intersection with $\\pi$ of a line which is perpendicular to $\\pi$ and which contains point $P$.</p>", "statement": "<p>Calculate the distance from point $P$ to the plane $\\pi$ given by:</p>", "ungrouped_variables": ["px", "py", "pz", "a", "b", "c", "d"], "type": "question", "contributors": [{"name": "Manuel P\u00e9rez", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1509/"}]}]}], "contributors": [{"name": "Manuel P\u00e9rez", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1509/"}]}