Vectors
(the database of solved problems)
All the problems and solutions shown below were generated using the Vectors Calculator.
| ID |
Problem |
Count |
| 6351 | Find the difference of the vectors $ \vec{v_1} = \left(2,~-4\right) $ and $ \vec{v_2} = \left(-4,~4\right) $ . | 1 |
| 6352 | Find the sum of the vectors $ \vec{v_1} = \left(2,~2\right) $ and $ \vec{v_2} = \left(-1,~1\right) $ . | 1 |
| 6353 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-1,~2,~1\right) $ and $ \vec{v_2} = \left(1,~3,~-1\right) $ . | 1 |
| 6354 | Find the magnitude of the vector $ \| \vec{v} \| = \left(10,~0\right) $ . | 1 |
| 6355 | Find the magnitude of the vector $ \| \vec{v} \| = \left(1,~-5\right) $ . | 1 |
| 6356 | Find the projection of the vector $ \vec{v_1} = \left(\dfrac{ 1 }{ 5 },~\dfrac{ 4 }{ 5 }\right) $ on the vector $ \vec{v_2} = \left(\dfrac{ 7 }{ 10 },~\dfrac{ 3 }{ 10 }\right) $. | 1 |
| 6357 | Find the magnitude of the vector $ \| \vec{v} \| = \left(\dfrac{ 1 }{ 5 },~\dfrac{ 4 }{ 5 }\right) $ . | 1 |
| 6358 | Calculate the dot product of the vectors $ \vec{v_1} = \left(5,~2\right) $ and $ \vec{v_2} = \left(7,~3\right) $ . | 1 |
| 6359 | Find the sum of the vectors $ \vec{v_1} = \left(3,~2\right) $ and $ \vec{v_2} = \left(2,~3\right) $ . | 1 |
| 6360 | Determine whether the vectors $ \vec{v_1} = \left(1,~0,~-1\right) $, $ \vec{v_2} = \left(2,~2,~2\right) $ and $ \vec{v_3} = \left(0,~-1,~1\right)$ are linearly independent or dependent. | 1 |
| 6361 | Find the angle between vectors $ \left(4,~3\right)$ and $\left(-2,~5\right)$. | 1 |
| 6362 | Find the magnitude of the vector $ \| \vec{v} \| = \left(1,~1,~1\right) $ . | 1 |
| 6363 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~1,~1\right) $ and $ \vec{v_2} = \left(2,~-1,~-1\right) $ . | 1 |
| 6364 | Calculate the dot product of the vectors $ \vec{v_1} = \left(0,~3,~-3\right) $ and $ \vec{v_2} = \left(3,~2,~-1\right) $ . | 1 |
| 6365 | Find the magnitude of the vector $ \| \vec{v} \| = \left(5,~13\right) $ . | 1 |
| 6366 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-2,~\dfrac{ 2 }{ 3 },~-3\right) $ and $ \vec{v_2} = \left(4,~0,~-\dfrac{ 1 }{ 2 }\right) $ . | 1 |
| 6367 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-64,~-3,~33\right) $ and $ \vec{v_2} = \left(0,~-3,~2\right) $ . | 1 |
| 6368 | Calculate the cross product of the vectors $ \vec{v_1} = \left(0,~0,~0\right) $ and $ \vec{v_2} = \left(0,~-3,~2\right) $ . | 1 |
| 6369 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-64,~-3,~33\right) $ and $ \vec{v_2} = \left(0,~-3,~2\right) $ . | 1 |
| 6370 | Calculate the cross product of the vectors $ \vec{v_1} = \left(93,~128,~92\right) $ and $ \vec{v_2} = \left(4,~-2,~3\right) $ . | 1 |
| 6371 | Find the sum of the vectors $ \vec{v_1} = \left(5,~0\right) $ and $ \vec{v_2} = \left(1,~4\right) $ . | 1 |
| 6372 | Find the projection of the vector $ \vec{v_1} = \left(5,~0\right) $ on the vector $ \vec{v_2} = \left(1,~4\right) $. | 1 |
| 6373 | Find the sum of the vectors $ \vec{v_1} = \left(1,~2\right) $ and $ \vec{v_2} = \left(3,~5\right) $ . | 1 |
| 6374 | Find the difference of the vectors $ \vec{v_1} = \left(3,~-5\right) $ and $ \vec{v_2} = \left(-1,~7\right) $ . | 1 |
| 6375 | Find the sum of the vectors $ \vec{v_1} = \left(3,~-5\right) $ and $ \vec{v_2} = \left(-1,~7\right) $ . | 1 |
| 6376 | Find the magnitude of the vector $ \| \vec{v} \| = \left(0,~0\right) $ . | 1 |
| 6377 | Find the magnitude of the vector $ \| \vec{v} \| = \left(17,~0\right) $ . | 1 |
| 6378 | Find the angle between vectors $ \left(17,~0\right)$ and $\left(17,~-16\right)$. | 1 |
| 6379 | Find the sum of the vectors $ \vec{v_1} = \left(-3,~3\right) $ and $ \vec{v_2} = \left(3,~4\right) $ . | 1 |
| 6380 | Find the sum of the vectors $ \vec{v_1} = \left(-1,~4\right) $ and $ \vec{v_2} = \left(6,~-2\right) $ . | 1 |
| 6381 | Find the magnitude of the vector $ \| \vec{v} \| = \left(20,~-15,~0\right) $ . | 1 |
| 6382 | Calculate the dot product of the vectors $ \vec{v_1} = \left(20,~-15,~0\right) $ and $ \vec{v_2} = \left(0,~0,~0\right) $ . | 1 |
| 6383 | Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~0\right) $ and $ \vec{v_2} = \left(1,~3\right) $ . | 1 |
| 6384 | Find the angle between vectors $ \left(2,~7\right)$ and $\left(7,~1\right)$. | 1 |
| 6385 | Find the angle between vectors $ \left(9,~-5\right)$ and $\left(6,~5\right)$. | 1 |
| 6386 | Find the magnitude of the vector $ \| \vec{v} \| = \left(\dfrac{ 23 }{ 2 },~\dfrac{ 413 }{ 10 }\right) $ . | 1 |
| 6387 | Find the difference of the vectors $ \vec{v_1} = \left(132163,~20000,~15950\right) $ and $ \vec{v_2} = \left(130569,~20309,~13986\right) $ . | 1 |
| 6388 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-3,~4\right) $ . | 1 |
| 6389 | Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~0\right) $ and $ \vec{v_2} = \left(2,~8\right) $ . | 1 |
| 6390 | Calculate the cross product of the vectors $ \vec{v_1} = \left(0,~-5,~5\right) $ and $ \vec{v_2} = \left(4,~2,~-5\right) $ . | 1 |
| 6391 | Find the difference of the vectors $ \vec{v_1} = \left(6,~2,~-2\right) $ and $ \vec{v_2} = \left(-1,~2,~4\right) $ . | 1 |
| 6392 | Find the difference of the vectors $ \vec{v_1} = \left(6,~2,~-4\right) $ and $ \vec{v_2} = \left(-1,~2,~4\right) $ . | 1 |
| 6393 | Find the magnitude of the vector $ \| \vec{v} \| = \left(1,~5,~-1\right) $ . | 1 |
| 6394 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~5,~-1\right) $ and $ \vec{v_2} = \left(5,~-1,~1\right) $ . | 1 |
| 6395 | Find the magnitude of the vector $ \| \vec{v} \| = \left(5,~-1,~1\right) $ . | 1 |
| 6396 | Find the sum of the vectors $ \vec{v_1} = \left(0.125,~0.1111\right) $ and $ \vec{v_2} = \left(0.875,~0.8889\right) $ . | 1 |
| 6397 | Find the projection of the vector $ \vec{v_1} = \left(1,~2,~4\right) $ on the vector $ \vec{v_2} = \left(1,~3,~5\right) $. | 1 |
| 6398 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~2,~4\right) $ and $ \vec{v_2} = \left(1,~3,~5\right) $ . | 1 |
| 6399 | Determine whether the vectors $ \vec{v_1} = \left(1,~1,~2\right) $, $ \vec{v_2} = \left(2,~3,~1\right) $ and $ \vec{v_3} = \left(4,~5,~5\right)$ are linearly independent or dependent. | 1 |
| 6400 | Find the magnitude of the vector $ \| \vec{v} \| = \left(4,~2,~2\right) $ . | 1 |
