\\\-3\\end{pmatrix}$ represent?","back":"4 units to the right.","points":1,"mcqOptions":null},{"id":"8f247bdc-e33d-4291-983a-947f41b5e99b","cardType":"basic","front":"What are the coordinates of a point with position vector $\\begin{pmatrix}-4\\\\7\\end{pmatrix}$?","back":"$(-4,7)$.","points":1,"mcqOptions":null},{"id":"22009140-5dbb-4f34-bb29-014473069bd8","cardType":"cloze","front":"A position vector always starts at the [ ].","back":"A position vector always starts at the origin.","points":null,"mcqOptions":null},{"id":"699fe301-e428-46db-9f8a-e8df0fb6f776","cardType":"basic","front":"Write the position vector of $A(3,-2)$.","back":"$\\begin{pmatrix}3\\\\-2\\end{pmatrix}$.","points":1,"mcqOptions":null},{"id":"fe8cfb02-9cb9-4707-bc51-44a955775727","cardType":"cloze","front":"The length of $\\mathbf v$ is its [ ], written $|\\mathbf v|$.","back":"The length of $\\mathbf v$ is its magnitude, written $|\\mathbf v|$.","points":null,"mcqOptions":null},{"id":"e71ce755-411c-437c-a454-6bf8f0fce468","cardType":"cloze","front":"For $\\mathbf v=\\begin{pmatrix}x\\\\y\\end{pmatrix}$, $\\text{[...]}$.","back":"For $\\mathbf v=\\begin{pmatrix}x\\\\y\\end{pmatrix}$, $\\boxed{|\\mathbf v|=\\sqrt{x^2+y^2}}$.","points":null,"mcqOptions":null},{"id":"7bc5b010-9d81-4f0f-a513-e3a176abc92d","cardType":"basic","front":"Why does a negative vector component contribute positively to its magnitude?","back":"The component is squared.","points":2,"mcqOptions":null},{"id":"f07f5351-d2f9-4cc6-ae7a-bd1f1f9008d1","cardType":"basic","front":"Calculate the magnitude of $\\begin{pmatrix}-5\\\\12\\end{pmatrix}$.","back":"$13$.","points":2,"mcqOptions":null},{"id":"f639166f-5d6c-45ac-b220-8e69fbce0681","cardType":"cloze","front":"If $A$ and $B$ have position vectors $\\mathbf a$ and $\\mathbf b$, then $\\text{[...]}$.","back":"If $A$ and $B$ have position vectors $\\mathbf a$ and $\\mathbf b$, then $\\boxed{\\overrightarrow{AB}=\\mathbf b-\\mathbf a}$.","points":null,"mcqOptions":null},{"id":"7eac50d2-6b28-40cb-b4b2-9a3b37cde747","cardType":"basic","front":"Given $\\mathbf a=\\begin{pmatrix}2\\\\-1\\end{pmatrix}$ and $\\mathbf b=\\begin{pmatrix}7\\\\3\\end{pmatrix}$, find $\\overrightarrow{AB}$.","back":"$\\begin{pmatrix}5\\\\4\\end{pmatrix}$.","points":2,"mcqOptions":null},{"id":"6046544d-0a49-4910-af0c-db361a382d47","cardType":"basic","front":"If $\\overrightarrow{AB}=\\mathbf v$, what is $\\overrightarrow{BA}$?","back":"$-\\mathbf v$.","points":1,"mcqOptions":null},{"id":"b9f5e06a-faab-44d8-9a4f-702192868afc","cardType":"cloze","front":"The distance between $A$ and $B$ is $\\text{[...]}$.","back":"The distance between $A$ and $B$ is $\\boxed{AB=|\\mathbf b-\\mathbf a|}$.","points":null,"mcqOptions":null},{"id":"5a6803af-7d9b-491c-a666-9166604b5316","cardType":"basic","front":"Is the distance between two points a scalar or a vector?","back":"A non-negative scalar.","points":1,"mcqOptions":null},{"id":"d1bb8c53-6470-40d5-b319-54f77478dd58","cardType":"basic","front":"For $\\mathbf p=\\begin{pmatrix}-2\\\\5\\end{pmatrix}$ and $\\mathbf q=\\begin{pmatrix}4\\\\1\\end{pmatrix}$, find the exact distance $PQ$.","back":"$2\\sqrt{13}$.","points":2,"mcqOptions":null},{"id":"582974c6-dc4a-4c08-95f9-18df7646ded8","cardType":"cloze","front":"In three dimensions, $\\text{[...]}$.","back":"In three dimensions, $\\boxed{AB=\\sqrt{(b_1-a_1)^2+(b_2-a_2)^2+(b_3-a_3)^2}}$.","points":null,"mcqOptions":null},{"id":"714ca7ef-8101-4daa-84b0-b12469fabbc8","cardType":"basic","front":"Find the distance between points with position vectors $\\begin{pmatrix}1\\\\-2\\\\4\\end{pmatrix}$ and $\\begin{pmatrix}5\\\\1\\\\-4\\end{pmatrix}$.","back":"$\\sqrt{89}$.","points":2,"mcqOptions":null},{"id":"de51f

1.9.3 Vectors Flashcards

1.9.3 Vectors Flashcards