// Numbas version: finer_feedback_settings
{"name": "Angle between two vectors", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"parts": [{"variableReplacements": [], "showCorrectAnswer": true, "prompt": "<p>Angle in degrees = [[0]]$^{\\circ}$</p>\n<p>Angle in radians = [[1]]radians.</p>\n<p>Note that you can input the radians as a decimal to 4 decimal places or as a <g class=\"gr_ gr_6 gr-alert gr_spell gr_inline_cards gr_run_anim ContextualSpelling ins-del multiReplace\" id=\"6\" data-gr-id=\"6\">mulptiple</g> of $\\pi$. You input $\\pi$ as pi.</p>", "marks": 0, "unitTests": [], "scripts": {}, "extendBaseMarkingAlgorithm": true, "customMarkingAlgorithm": "", "sortAnswers": false, "type": "gapfill", "variableReplacementStrategy": "originalfirst", "gaps": [{"variableReplacements": [], "showCorrectAnswer": true, "notationStyles": ["plain", "en", "si-en"], "marks": 1, "unitTests": [], "scripts": {}, "mustBeReducedPC": 0, "correctAnswerStyle": "plain", "mustBeReduced": false, "extendBaseMarkingAlgorithm": true, "allowFractions": false, "correctAnswerFraction": false, "maxValue": "{angle}", "customMarkingAlgorithm": "", "type": "numberentry", "variableReplacementStrategy": "originalfirst", "minValue": "{angle}", "showFeedbackIcon": true}, {"variableReplacements": [], "showCorrectAnswer": true, "marks": 1, "unitTests": [], "scripts": {}, "checkingType": "absdiff", "expectedVariableNames": [], "answer": "{precround(angle*pi/180,4)}", "vsetRange": [0, 1], "extendBaseMarkingAlgorithm": true, "checkingAccuracy": 0.0001, "customMarkingAlgorithm": "", "type": "jme", "vsetRangePoints": 5, "variableReplacementStrategy": "originalfirst", "showPreview": true, "checkVariableNames": false, "failureRate": 1, "showFeedbackIcon": true}], "showFeedbackIcon": true}], "functions": {}, "advice": "<p>Bruker formelen:</p>\n  <p>$\\boldsymbol{A \\cdot B} = |\\boldsymbol{A}||\\boldsymbol{B}|\\cos(\\theta)$ der $\\theta$ er vinkelen mellom vektorene.</p>\n  <p>Her er $|\\boldsymbol{A}| = \\sqrt{ (\\var{s1})^2+(\\var{s2})^2} = \\simplify[all]{sqrt({s1^2+s2^2})},\\;\\;\\;|\\boldsymbol{B}| = \\sqrt{ (\\var{s3})^2+(\\var{s4})^2} = \\simplify[all]{sqrt({s3^2+s4^2})}$</p>\n  <p>og</p>\n  <p>$\\boldsymbol{A \\cdot B} = (\\var{fa},\\var{sa}, \\var{ta}) \\cdot (\\var{fb},\\var{sb}, \\var{tb}) = \\var{g}$.</p>\n  <p>Slik at \\[\\begin{eqnarray*} \\cos(\\theta)&amp;=&amp;\\frac{\\var{g}}{\\sqrt{2}\\sqrt{2}} = \\simplify[std]{{g}/{2}}\\\\ \\Rightarrow \\theta &amp;=&amp;\\arccos\\left(\\simplify[std]{{g}/{2}}\\right)\\\\ &amp;=&amp;\\var{angle}\\,^{\\circ} \\end{eqnarray*} \\]<br/>Konvertering fra grader til radianer gj&oslash;res ved &aring; multiplisere vinkel i grader med $\\displaystyle \\frac{\\pi}{180}$.</p>\n  <p>Da blir $\\displaystyle \\var{angle}\\,^{\\circ}=\\simplify[std]{({angle}*pi)/{180}= {precround(angle*pi/180,4)}}$ radianer i 4 siffers n&oslash;yaktighet.</p>", "statement": "<p>Given the vectors<br/>$\\mathbf{a}=\\var{fa}\\mathbf{i}+\\var{sa}\\mathbf{j}+\\var{ta}\\mathbf{k},\\;\\;\\;\\mathbf{b}=\\var{fb}\\mathbf{i}+\\var{sb}\\mathbf{j}+ \\var{tb}\\mathbf{k}$</p>\n<p>Find the angle between these vectors in degrees and radians.</p>\n<p>Note that the angle must be between $0\\,^{\\circ}$ and $180\\,^{\\circ}$ (between $0$ and $\\pi$ radians)</p>", "tags": [], "preamble": {"js": "", "css": ""}, "ungrouped_variables": ["s1", "a", "s4", "fa", "angle", "g", "fb", "tb", "sb", "ta", "c", "sa", "s2", "s3", "u", "d", "b", "t"], "extensions": [], "variables": {"a": {"definition": "if(t=1,2,1)", "group": "Ungrouped variables", "templateType": "anything", "description": "", "name": "a"}, "s4": {"definition": "if(s1=s3 ,-s2,random(-1,1))", "group": "Ungrouped variables", "templateType": "anything", "description": "", "name": "s4"}, "fa": {"definition": "if(t=1,0,s1)", "group": "Ungrouped variables", "templateType": "anything", "description": "", "name": "fa"}, "angle": {"definition": "precround(180/pi*arccos(g/2),1)", "group": "Ungrouped variables", "templateType": "anything", "description": "", "name": "angle"}, "s1": {"definition": "random(1,-1)", "group": "Ungrouped variables", "templateType": "anything", "description": "", "name": "s1"}, "fb": {"definition": "if(u=1,0,s3)", "group": "Ungrouped variables", "templateType": "anything", "description": "", "name": "fb"}, "tb": {"definition": "if(u=3,0,s4)", "group": "Ungrouped variables", "templateType": "anything", "description": "", "name": "tb"}, "sb": {"definition": "if(u=2,0,if(u=1,s3,s4))", "group": "Ungrouped variables", "templateType": "anything", "description": "", "name": "sb"}, "ta": {"definition": "if(t=3,0,s2)", "group": "Ungrouped variables", "templateType": "anything", "description": "", "name": "ta"}, "c": {"definition": "if(u=1,2,1)", "group": "Ungrouped variables", "templateType": "anything", "description": "", "name": "c"}, "sa": {"definition": "if(t=2,0,if(t=1,s1,s2))", "group": "Ungrouped variables", "templateType": "anything", "description": "", "name": "sa"}, "s2": {"definition": "random(1,-1)", "group": "Ungrouped variables", "templateType": "anything", "description": "", "name": "s2"}, "s3": {"definition": "random(1,-1)", "group": "Ungrouped variables", "templateType": "anything", "description": "", "name": "s3"}, "u": {"definition": "random(1,2,3)", "group": "Ungrouped variables", "templateType": "anything", "description": "", "name": "u"}, "d": {"definition": "if(u=3,2,3)", "group": "Ungrouped variables", "templateType": "anything", "description": "", "name": "d"}, "b": {"definition": "if(t=3,2,3)", "group": "Ungrouped variables", "templateType": "anything", "description": "", "name": "b"}, "g": {"definition": "{fa*fb+sa*sb+ta*tb}", "group": "Ungrouped variables", "templateType": "anything", "description": "", "name": "g"}, "t": {"definition": "random(1,2,3)", "group": "Ungrouped variables", "templateType": "anything", "description": "", "name": "t"}}, "variablesTest": {"condition": "", "maxRuns": 100}, "metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": "<p>Find the angle between two vectors</p>"}, "name": "Angle between two vectors", "rulesets": {"std": ["all", "fractionNumbers", "!collectNumbers", "!noLeadingMinus"]}, "variable_groups": [], "type": "question", "contributors": [{"name": "Julie Crowley", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/113/"}, {"name": "Marie Nicholson", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1799/"}]}]}], "contributors": [{"name": "Julie Crowley", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/113/"}, {"name": "Marie Nicholson", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1799/"}]}