// Numbas version: exam_results_page_options
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In this case,&nbsp;let $\\bf a$, $\\bf b$ and $\\bf c$ be the position vectors of $A$, $B$, and $C$, such that&nbsp;</p>\n<p>\\[ \\mathbf a = \\var{a}, \\quad&nbsp;\\mathbf b = \\var{b}, \\quad&nbsp;\\mathbf c = \\var{c}.\\]</p>\n<p>{geogebra_applet('https://www.geogebra.org/m/jrrcctdj',defs)}</p>\n<p>To find the vector $\\vec{AB}$, consider how you can get between $A$ and $B$ only 'travelling' along the position vectors. Firstly, we need to go from $A$ to the origin $O$, which is the vector $\\mathbf{-a}$, and then from the $O$ to $B$, which is the vector $\\mathbf b$. Therefore, $\\vec{AB} = \\mathbf{-a}+\\mathbf{b}$, or more simply, \\[ \\vec{AB} = \\mathbf {b} - \\mathbf{a}.\\] The same method applies for finding the vectors $\\vec{AC}$ and $\\vec{CB}$.</p>\n<p>Therefore,</p>\n<p>\\[ \\vec{AB} = \\mathbf{b}-\\mathbf{a} = \\var{sola}, \\]</p>\n<p>\\[ \\vec{AC} = \\mathbf{c}-\\mathbf{a} = \\var{solb}, \\]</p>\n<p>\\[ \\vec{CB} = \\mathbf{b}-\\mathbf{c} = \\var{solc}, \\]</p>\n<p></p>", "rulesets": {}, "extensions": ["geogebra"], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"a": {"name": "a", "group": "Ungrouped variables", "definition": "vector(random(-5..-3),random(2..3))", "description": "", "templateType": "anything", "can_override": false}, "b": {"name": "b", "group": "Ungrouped variables", "definition": "vector(random(2..5),random(3..4 except a[1]))", "description": "", "templateType": "anything", "can_override": false}, "c": {"name": "c", "group": "Ungrouped variables", "definition": 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"customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>$\\vec{AB}$</p>\n<p>[[0]]</p>", "gaps": [{"type": "matrix", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "correctAnswer": "vector(sola[0],sola[1])", "correctAnswerFractions": false, "numRows": "2", "numColumns": 1, "allowResize": false, "tolerance": 0, "markPerCell": false, "allowFractions": 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