nsions Flashcards","topicId":"fa12888a-4621-44b5-9c28-fe2abf959d0f","topicSlug":"vectors-in-two-dimensions","cards":[{"id":"da6f80ba-902b-4930-b8c9-e58c7a3bb5a7","cardType":"basic","front":"Why is “walk 5 m east” a vector rather than a scalar?","back":"It specifies both magnitude and direction.","points":2,"mcqOptions":null},{"id":"87b6f6ee-e556-42b2-ada5-4044b05efbb3","cardType":"basic","front":"What movement does $\\begin{pmatrix}-4\\\\3\\end{pmatrix}$ represent?","back":"4 units left and 3 units up.","points":1,"mcqOptions":null},{"id":"93bf4ede-0360-45c0-be13-2f62824c8293","cardType":"basic","front":"What displacement is represented by $\\overrightarrow{AB}$?","back":"The displacement from $A$ to $B$.","points":1,"mcqOptions":null},{"id":"a2b232a3-c454-4d51-9e42-a602faa95d15","cardType":"cloze","front":"Reversing a directed vector gives $\\overrightarrow{BA}=$ $\\text{[...]}$.","back":"Reversing a directed vector gives $\\overrightarrow{BA}=$ $\\boxed{-\\overrightarrow{AB}}$.","points":null,"mcqOptions":null},{"id":"c0c931a9-cda6-4a60-b201-4f6c589baaec","cardType":"basic","front":"Write $4\\mathbf{i}-7\\mathbf{j}$ as a column vector.","back":"$\\begin{pmatrix}4\\\\-7\\end{pmatrix}$","points":1,"mcqOptions":null},{"id":"c88cd6fa-39ff-45b9-92e7-0ae4741a23ea","cardType":"cloze","front":"The unit vectors are $\\mathbf{i}=\\begin{pmatrix}1\\\\0\\end{pmatrix}$ and $\\text{[...]}$.","back":"The unit vectors are $\\mathbf{i}=\\begin{pmatrix}1\\\\0\\end{pmatrix}$ and $\\boxed{\\mathbf{j}=\\begin{pmatrix}0\\\\1\\end{pmatrix}}$.","points":null,"mcqOptions":null},{"id":"481de15d-34cb-43f0-97ba-a19352d018d6","cardType":"basic","front":"Calculate $\\begin{pmatrix}3\\\\-2\\end{pmatrix}+\\begin{pmatrix}-5\\\\6\\end{pmatrix}$.","back":"$\\begin{pmatrix}-2\\\\4\\end{pmatrix}$","points":1,"mcqOptions":null},{"id":"f8339992-8b0a-4c3e-a143-11a2301aedb2","cardType":"cloze","front":"Following the route $A$ to $B$ to $C$ gives $\\text{[...]}$.","back":"Following the route $A$ to $B$ to $C$ gives $\\boxed{\\overrightarrow{AB}+\\overrightarrow{BC}=\\overrightarrow{AC}}$.","points":null,"mcqOptions":null},{"id":"9606da1e-acc8-4232-808c-a63cef85c147","cardType":"basic","front":"Calculate $3\\begin{pmatrix}-2\\\\5\\end{pmatrix}$.","back":"$\\begin{pmatrix}-6\\\\15\\end{pmatrix}$","points":1,"mcqOptions":null},{"id":"28afeaef-61f2-452b-8136-28b071098f8a","cardType":"basic","front":"How does multiplying a non-zero vector by a negative scalar affect it?","back":"Its magnitude is scaled and direction reversed.","points":2,"mcqOptions":null},{"id":"6b96f2de-71d2-4e08-9eac-c61dbffaf56b","cardType":"cloze","front":"For $\\mathbf{a}=\\begin{pmatrix}x\\\\y\\end{pmatrix}$, its magnitude is $\\text{[...]}$.","back":"For $\\mathbf{a}=\\begin{pmatrix}x\\\\y\\end{pmatrix}$, its magnitude is $\\boxed{|\\mathbf{a}|=\\sqrt{x^2+y^2}}$.","points":null,"mcqOptions":null},{"id":"e0a265a8-72df-4ae3-adf2-9646135e42e2","cardType":"basic","front":"Find the magnitude of $\\begin{pmatrix}-5\\\\12\\end{pmatrix}$.","back":"$13$","points":2,"mcqOptions":null},{"id":"07bb5aaf-c67c-4c5f-b4f4-60ab7cdcc4d2","cardType":"basic","front":"Find a unit vector in the direction of $\\begin{pmatrix}3\\\\-4\\end{pmatrix}$.","back":"$\\begin{pmatrix}\\frac{3}{5}\\\\-\\frac{4}{5}\\end{pmatrix}$","points":2,"mcqOptions":null},{"id":"8e5a0b4e-49ea-498c-91d7-58a15efce74f","cardType":"basic","front":"Why can no unit vector be formed from $\\mathbf{0}$?","back":"Its magnitude is zero, so division by it is undefined.","points":2,"mcqOptions":null},{"id":"f6ef3c04-b136-46bd-a3f2-ac1bf96a7a07","cardType":"cloze","front":"A unit vector in the direction of non-zero $\\mathbf{a}$ is $\\text{[...]}$.","back":"A unit vector in the direction of non-zero $\\mathbf{a}$ is $\\boxed{\\widehat{\\mathbf{a}}=\\frac{\\mathbf{a}}{|\\mathbf{a}|}}$.","points":null,"mcqOptions":null},{"id":"9d35132e-89f3-4466-88ba-89c9195118b8","cardType":"basic

1.10.1 Vectors in two dimensions Flashcards

1.10.1 Vectors in two dimensions Flashcards