ving using vectors Flashcards","topicId":"d4956b49-cba4-47ee-b526-d36350aa60d9","topicSlug":"problem-solving-using-vectors","cards":[{"id":"4718bf9d-f5ee-435b-8a3a-83476fa313e0","cardType":"cloze","front":"The entries in a column vector are its horizontal and vertical [ ].","back":"The entries in a column vector are its horizontal and vertical components.","points":null,"mcqOptions":null},{"id":"9b157dae-fff1-4aa1-921a-ae1226eac687","cardType":"basic","front":"Calculate $\\begin{pmatrix}5\\\\-2\\end{pmatrix}+\\begin{pmatrix}-1\\\\7\\end{pmatrix}$.","back":"$$\\begin{pmatrix}4\\\\5\\end{pmatrix}$","points":1,"mcqOptions":null},{"id":"2cc8fe5e-809b-45d4-8b47-16ace9831268","cardType":"basic","front":"What happens to a vector's direction when it is multiplied by a negative scalar?","back":"Its direction is reversed.","points":1,"mcqOptions":null},{"id":"c166ff40-053f-4b82-87b3-a13946c68a79","cardType":"cloze","front":"Following a route from $A$ through $B$ to $C$ gives $\\text{[...]}$.","back":"Following a route from $A$ through $B$ to $C$ gives $\\boxed{\\overrightarrow{AB}+\\overrightarrow{BC}=\\overrightarrow{AC}}$.","points":null,"mcqOptions":null},{"id":"11defe4c-074d-469a-b94d-50fc18a2277c","cardType":"basic","front":"A displacement is $\\begin{pmatrix}4\\\\5\\end{pmatrix}$ m. Interpret its horizontal component.","back":"The particle moves 4 m to the right.","points":1,"mcqOptions":null},{"id":"d4bd0344-15f3-4653-8a45-64b660cc155d","cardType":"cloze","front":"A vector from one point to another is found using [ ].","back":"A vector from one point to another is found using finish minus start.","points":null,"mcqOptions":null},{"id":"a9e20129-6ac2-44ff-92f1-98991e85b9c1","cardType":"basic","front":"If $\\overrightarrow{OA}=\\mathbf a$ and $\\overrightarrow{OB}=\\mathbf b$, what is $\\overrightarrow{AB}$?","back":"$$\\mathbf b-\\mathbf a$","points":1,"mcqOptions":null},{"id":"e5b8711a-73fd-4dfe-9f89-16fe28540925","cardType":"basic","front":"What vector results if the subtraction for $\\overrightarrow{AB}$ is reversed?","back":"$$\\overrightarrow{BA}$, which points in the opposite direction.","points":1,"mcqOptions":null},{"id":"28357895-764f-4a88-b8d6-c17fbc4ed165","cardType":"basic","front":"If $\\mathbf a=\\begin{pmatrix}2\\\\-1\\end{pmatrix}$ and $\\mathbf b=\\begin{pmatrix}8\\\\5\\end{pmatrix}$, find $\\overrightarrow{AB}$.","back":"$$\\begin{pmatrix}6\\\\6\\end{pmatrix}$","points":1,"mcqOptions":null},{"id":"364ff4da-335e-40b6-add2-93b79aff0230","cardType":"basic","front":"Express the position vector of the midpoint of $AB$ using $\\mathbf a$ and $\\mathbf b$.","back":"$$\\frac12(\\mathbf a+\\mathbf b)$","points":1,"mcqOptions":null},{"id":"f3eea962-d825-41aa-b235-b8cdf2ad4461","cardType":"basic","front":"If $AP:PB=m:n$, what fraction of the journey from $A$ to $B$ is $AP$?","back":"$$\\frac{m}{m+n}$","points":1,"mcqOptions":null},{"id":"14bb7c1e-c9c2-4fab-a4da-cb4e27e80c73","cardType":"basic","front":"Express $\\overrightarrow{OP}$ when $P$ divides $AB$ in the ratio $AP:PB=2:3$.","back":"$$\\frac35\\mathbf a+\\frac25\\mathbf b$","points":2,"mcqOptions":null},{"id":"7c08e9c9-a901-48dc-b6f2-9d93d13c2f28","cardType":"basic","front":"Express the position vector of the point three-quarters of the way from $A$ to $B$.","back":"$$\\mathbf a+\\frac34(\\mathbf b-\\mathbf a)$","points":2,"mcqOptions":null},{"id":"1b222ef2-7ba2-42c4-9fdd-e1bfa95aeabb","cardType":"cloze","front":"To prove $A$, $B$ and $C$ are collinear, show that $\\text{[...]}$ for some scalar $k$.","back":"To prove $A$, $B$ and $C$ are collinear, show that $\\boxed{\\overrightarrow{AC}=k\\overrightarrow{AB}}$ for some scalar $k$.","points":null,"mcqOptions":null},{"id":"94a1ae18-06d5-40bc-8c99-5f74a7fb3296","cardType":"basic","front":"Why does $\\overrightarrow{AC}=k\\overrightarrow{AB}$ prove

1.10.7 Problem solving using vectors Flashcards

1.10.7 Problem solving using vectors Flashcards