Vectors – Solved Problems Database
All the problems and solutions shown below were generated using the Vectors Calculator.
ID |
Problem |
Count |
251 | Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~-2\right) $ and $ \vec{v_2} = \left(5,~1\right) $ . | 3 |
252 | | 3 |
253 | Find the difference of the vectors $ \vec{v_1} = \left(2,~4\right) $ and $ \vec{v_2} = \left(6,~5\right) $ . | 3 |
254 | Determine whether the vectors $ \vec{v_1} = \left(2,~1\right) $ and $ \vec{v_2} = \left(1,~2\right) $ are linearly independent or dependent. | 3 |
255 | Find the angle between vectors $ \left(\dfrac{\sqrt{ 3 }}{ 2 },~\dfrac{ 1 }{ 2 }\right)$ and $\left(- \dfrac{\sqrt{ 2 }}{ 2 },~- \dfrac{\sqrt{ 2 }}{ 2 }\right)$. | 3 |
256 | Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~2\right) $ and $ \vec{v_2} = \left(-7,~6\right) $ . | 3 |
257 | Find the angle between vectors $ \left(7,~-1\right)$ and $\left(2,~2\right)$. | 3 |
258 | Find the sum of the vectors $ \vec{v_1} = \left(-2,~10\right) $ and $ \vec{v_2} = \left(6,~12\right) $ . | 3 |
259 | Find the projection of the vector $ \vec{v_1} = \left(6,~7\right) $ on the vector $ \vec{v_2} = \left(0,~0\right) $. | 3 |
260 | Find the difference of the vectors $ \vec{v_1} = \left(4,~-7\right) $ and $ \vec{v_2} = \left(-13,~12\right) $ . | 3 |
261 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~1\right) $ and $ \vec{v_2} = \left(\dfrac{ 34641 }{ 20000 },~3\right) $ . | 3 |
262 | Calculate the dot product of the vectors $ \vec{v_1} = \left(6,~-4\right) $ and $ \vec{v_2} = \left(-2,~5\right) $ . | 3 |
263 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-5,~5\right) $ . | 3 |
264 | Calculate the cross product of the vectors $ \vec{v_1} = \left(3,~-2,~7\right) $ and $ \vec{v_2} = \left(4,~3,~-2\right) $ . | 3 |
265 | Find the magnitude of the vector $ \| \vec{v} \| = \left(4,~5\right) $ . | 3 |
266 | Find the magnitude of the vector $ \| \vec{v} \| = \left(1,~1\right) $ . | 3 |
267 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-7,~3\right) $ and $ \vec{v_2} = \left(-5,~-6\right) $ . | 3 |
268 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-5,~1\right) $ and $ \vec{v_2} = \left(4,~-5\right) $ . | 3 |
269 | Find the magnitude of the vector $ \| \vec{v} \| = \left(7,~6\right) $ . | 3 |
270 | Find the difference of the vectors $ \vec{v_1} = \left(10,~0\right) $ and $ \vec{v_2} = \left(8,~-12\right) $ . | 3 |
271 | Find the magnitude of the vector $ \| \vec{v} \| = \left(2,~0,~0\right) $ . | 3 |
272 | Find the difference of the vectors $ \vec{v_1} = \left(-2,~3\right) $ and $ \vec{v_2} = \left(-3,~5\right) $ . | 3 |
273 | Find the sum of the vectors $ \vec{v_1} = \left(2,~2 \sqrt{ 3 }\right) $ and $ \vec{v_2} = \left(6,~0\right) $ . | 3 |
274 | Find the difference of the vectors $ \vec{v_1} = \left(2,~2 \sqrt{ 3 }\right) $ and $ \vec{v_2} = \left(-2,~0\right) $ . | 3 |
275 | Find the sum of the vectors $ \vec{v_1} = \left(3,~4\right) $ and $ \vec{v_2} = \left(-1,~1\right) $ . | 3 |
276 | Find the difference of the vectors $ \vec{v_1} = \left(1,~-5\right) $ and $ \vec{v_2} = \left(-2,~0\right) $ . | 3 |
277 | Find the angle between vectors $ \left(9,~-7\right)$ and $\left(8,~3\right)$. | 3 |
278 | Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~5\right) $ and $ \vec{v_2} = \left(4,~-3\right) $ . | 3 |
279 | Find the projection of the vector $ \vec{v_1} = \left(3,~4\right) $ on the vector $ \vec{v_2} = \left(8,~2\right) $. | 3 |
280 | Calculate the dot product of the vectors $ \vec{v_1} = \left(5,~-4\right) $ and $ \vec{v_2} = \left(-1,~2\right) $ . | 3 |
281 | Find the magnitude of the vector $ \| \vec{v} \| = \left(6,~8\right) $ . | 3 |
282 | Calculate the cross product of the vectors $ \vec{v_1} = \left(0,~0,~3\right) $ and $ \vec{v_2} = \left(\dfrac{ 3 }{ 2 },~0,~3\right) $ . | 3 |
283 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-\dfrac{ 211 }{ 50 },~\dfrac{ 267 }{ 50 }\right) $ . | 3 |
284 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-3,~4\right) $ . | 3 |
285 | Find the angle between vectors $ \left(-3,~-5\right)$ and $\left(-4,~-2\right)$. | 3 |
286 | Find the difference of the vectors $ \vec{v_1} = \left(\dfrac{ 173 }{ 10 },~10\right) $ and $ \vec{v_2} = \left(-\dfrac{ 63 }{ 10 },~\dfrac{ 68 }{ 5 }\right) $ . | 3 |
287 | Calculate the dot product of the vectors $ \vec{v_1} = \left(0,~4\right) $ and $ \vec{v_2} = \left(4,~1\right) $ . | 3 |
288 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-1,~2\right) $ . | 3 |
289 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-6,~12\right) $ . | 3 |
290 | Find the difference of the vectors $ \vec{v_1} = \left(3,~5\right) $ and $ \vec{v_2} = \left(\dfrac{ 22 }{ 5 },~\dfrac{ 11 }{ 5 }\right) $ . | 3 |
291 | Calculate the dot product of the vectors $ \vec{v_1} = \left(5,~2\right) $ and $ \vec{v_2} = \left(9,~8\right) $ . | 3 |
292 | Determine whether the vectors $ \vec{v_1} = \left(3,~12,~-21\right) $, $ \vec{v_2} = \left(2,~0,~4\right) $ and $ \vec{v_3} = \left(0,~-10,~20\right)$ are linearly independent or dependent. | 3 |
293 | Determine whether the vectors $ \vec{v_1} = \left(-7,~7\right) $ and $ \vec{v_2} = \left(1,~22\right) $ are linearly independent or dependent. | 3 |
294 | Find the magnitude of the vector $ \| \vec{v} \| = \left(4,~23\right) $ . | 3 |
295 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-3,~0\right) $ and $ \vec{v_2} = \left(-1,~1\right) $ . | 3 |
296 | Find the projection of the vector $ \vec{v_1} = \left(3,~6\right) $ on the vector $ \vec{v_2} = \left(-2,~9\right) $. | 3 |
297 | Find the magnitude of the vector $ \| \vec{v} \| = \left(1,~-6\right) $ . | 3 |
298 | Find the angle between vectors $ \left(2,~1\right)$ and $\left(6,~3\right)$. | 3 |
299 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-4,~3\right) $ . | 3 |
300 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-3 \sqrt{ 3 },~-3\right) $ . | 3 |