Vectors
(the database of solved problems)
All the problems and solutions shown below were generated using the Vectors Calculator.
| ID |
Problem |
Count |
| 5301 | Find the sum of the vectors $ \vec{v_1} = \left(3,~3\right) $ and $ \vec{v_2} = \left(0,~0\right) $ . | 1 |
| 5302 | Find the sum of the vectors $ \vec{v_1} = \left(3,~-4\right) $ and $ \vec{v_2} = \left(-4,~-7\right) $ . | 1 |
| 5303 | Find the magnitude of the vector $ \| \vec{v} \| = \left(17,~-33,~31\right) $ . | 1 |
| 5304 | Find the sum of the vectors $ \vec{v_1} = \left(-1,~-4\right) $ and $ \vec{v_2} = \left(-4,~7\right) $ . | 1 |
| 5305 | Find the sum of the vectors $ \vec{v_1} = \left(3,~-4\right) $ and $ \vec{v_2} = \left(-4,~7\right) $ . | 1 |
| 5306 | Find the angle between vectors $ \left(3,~-4\right)$ and $\left(-4,~7\right)$. | 1 |
| 5307 | Calculate the cross product of the vectors $ \vec{v_1} = \left(3,~-4,~0\right) $ and $ \vec{v_2} = \left(-4,~7,~0\right) $ . | 1 |
| 5308 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-2,~3\right) $ . | 1 |
| 5309 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-2,~3\right) $ . | 1 |
| 5310 | Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~-1\right) $ and $ \vec{v_2} = \left(-1,~3\right) $ . | 1 |
| 5311 | Find the sum of the vectors $ \vec{v_1} = \left(-6,~8\right) $ and $ \vec{v_2} = \left(6,~-3\right) $ . | 1 |
| 5312 | Find the difference of the vectors $ \vec{v_1} = \left(10,~8\right) $ and $ \vec{v_2} = \left(6,~2\right) $ . | 1 |
| 5313 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-2,~5\right) $ . | 1 |
| 5314 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-2,~5\right) $ and $ \vec{v_2} = \left(5,~-1\right) $ . | 1 |
| 5315 | Find the magnitude of the vector $ \| \vec{v} \| = \left(3,~4\right) $ . | 1 |
| 5316 | Find the magnitude of the vector $ \| \vec{v} \| = \left(0,~3\right) $ . | 1 |
| 5317 | Calculate the dot product of the vectors $ \vec{v_1} = \left(0,~3\right) $ and $ \vec{v_2} = \left(-1,~2\right) $ . | 1 |
| 5318 | Find the sum of the vectors $ \vec{v_1} = \left(4,~7\right) $ and $ \vec{v_2} = \left(3,~8\right) $ . | 1 |
| 5319 | Find the sum of the vectors $ \vec{v_1} = \left(7,~0\right) $ and $ \vec{v_2} = \left(3,~8\right) $ . | 1 |
| 5320 | Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~-2\right) $ and $ \vec{v_2} = \left(-1,~5\right) $ . | 1 |
| 5321 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-8,~2\right) $ and $ \vec{v_2} = \left(8,~2\right) $ . | 1 |
| 5322 | Find the angle between vectors $ \left(3,~8\right)$ and $\left(7,~-8\right)$. | 1 |
| 5323 | Find the magnitude of the vector $ \| \vec{v} \| = \left(8,~-15\right) $ . | 1 |
| 5324 | Find the angle between vectors $ \left(4,~0\right)$ and $\left(5,~-2\right)$. | 1 |
| 5325 | Find the angle between vectors $ \left(4,~-4\right)$ and $\left(5,~-4\right)$. | 1 |
| 5326 | Find the difference of the vectors $ \vec{v_1} = \left(-1,~4\right) $ and $ \vec{v_2} = \left(4,~5\right) $ . | 1 |
| 5327 | Find the sum of the vectors $ \vec{v_1} = \left(-47,~16\right) $ and $ \vec{v_2} = \left(10,~17\right) $ . | 1 |
| 5328 | Find the angle between vectors $ \left(3,~-1\right)$ and $\left(4,~7\right)$. | 1 |
| 5329 | Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~11\right) $ and $ \vec{v_2} = \left(5,~-1\right) $ . | 1 |
| 5330 | Find the projection of the vector $ \vec{v_1} = \left(7,~-3\right) $ on the vector $ \vec{v_2} = \left(1,~1\right) $. | 1 |
| 5331 | Find the sum of the vectors $ \vec{v_1} = \left(5,~-2\right) $ and $ \vec{v_2} = \left(4,~1\right) $ . | 1 |
| 5332 | Determine whether the vectors $ \vec{v_1} = \left(6,~-6\right) $ and $ \vec{v_2} = \left(-4,~6\right) $ are linearly independent or dependent. | 1 |
| 5333 | Find the magnitude of the vector $ \| \vec{v} \| = \left(7,~1,~-2\right) $ . | 1 |
| 5334 | Calculate the dot product of the vectors $ \vec{v_1} = \left(6,~1\right) $ and $ \vec{v_2} = \left(1,~-3\right) $ . | 1 |
| 5335 | Calculate the dot product of the vectors $ \vec{v_1} = \left(6,~1\right) $ and $ \vec{v_2} = \left(3,~4\right) $ . | 1 |
| 5336 | Find the magnitude of the vector $ \| \vec{v} \| = \left(\dfrac{ 1 }{ 5 },~\dfrac{ 4 }{ 5 }\right) $ . | 1 |
| 5337 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-3,~2,~3\right) $ . | 1 |
| 5338 | Find the sum of the vectors $ \vec{v_1} = \left(-3,~2,~3\right) $ and $ \vec{v_2} = \left(3,~-2,~-1\right) $ . | 1 |
| 5339 | Determine whether the vectors $ \vec{v_1} = \left(-3,~2,~3\right) $, $ \vec{v_2} = \left(3,~-2,~-1\right) $ and $ \vec{v_3} = \left(0,~10,~-5\right)$ are linearly independent or dependent. | 1 |
| 5340 | Find the sum of the vectors $ \vec{v_1} = \left(-2,~1\right) $ and $ \vec{v_2} = \left(4,~-3\right) $ . | 1 |
| 5341 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-2,~1\right) $ . | 1 |
| 5342 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-1,~3\right) $ . | 1 |
| 5343 | Calculate the cross product of the vectors $ \vec{v_1} = \left(2,~-1,~9\right) $ and $ \vec{v_2} = \left(7,~2,~1\right) $ . | 1 |
| 5344 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~0,~-9\right) $ and $ \vec{v_2} = \left(0,~1,~1\right) $ . | 1 |
| 5345 | Calculate the cross product of the vectors $ \vec{v_1} = \left(9,~0,~-3\right) $ and $ \vec{v_2} = \left(0,~7,~0\right) $ . | 1 |
| 5346 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~1,~0\right) $ and $ \vec{v_2} = \left(0,~0,~1\right) $ . | 1 |
| 5347 | Calculate the cross product of the vectors $ \vec{v_1} = \left(3,~0,~3\right) $ and $ \vec{v_2} = \left(-2,~1,~5\right) $ . | 1 |
| 5348 | Find the magnitude of the vector $ \| \vec{v} \| = \left(3,~0,~3\right) $ . | 1 |
| 5349 | Find the difference of the vectors $ \vec{v_1} = \left(-4,~-5\right) $ and $ \vec{v_2} = \left(-1,~0\right) $ . | 1 |
| 5350 | Find the sum of the vectors $ \vec{v_1} = \left(4,~6\right) $ and $ \vec{v_2} = \left(4,~1\right) $ . | 1 |
