Vectors
(the database of solved problems)
All the problems and solutions shown below were generated using the Vectors Calculator.
| ID |
Problem |
Count |
| 5401 | Find the magnitude of the vector $ \| \vec{v} \| = \left(9,~-2\right) $ . | 1 |
| 5402 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-1,~3,~1\right) $ and $ \vec{v_2} = \left(0,~1,~-1\right) $ . | 1 |
| 5403 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-1,~3,~1\right) $ and $ \vec{v_2} = \left(-1,~3,~1\right) $ . | 1 |
| 5404 | Find the projection of the vector $ \vec{v_1} = \left(-3,~2,~0\right) $ on the vector $ \vec{v_2} = \left(-4,~2,~0\right) $. | 1 |
| 5405 | Find the projection of the vector $ \vec{v_1} = \left(1,~2,~-1\right) $ on the vector $ \vec{v_2} = \left(-9,~0,~2\right) $. | 1 |
| 5406 | Find the projection of the vector $ \vec{v_1} = \left(1,~3,~-3\right) $ on the vector $ \vec{v_2} = \left(-7,~0,~3\right) $. | 1 |
| 5407 | Find the projection of the vector $ \vec{v_1} = \left(-7,~0,~3\right) $ on the vector $ \vec{v_2} = \left(1,~3,~-3\right) $. | 1 |
| 5408 | Find the projection of the vector $ \vec{v_1} = \left(1,~2,~-2\right) $ on the vector $ \vec{v_2} = \left(-9,~0,~2\right) $. | 1 |
| 5409 | Find the projection of the vector $ \vec{v_1} = \left(-4,~-1\right) $ on the vector $ \vec{v_2} = \left(-4,~1\right) $. | 1 |
| 5410 | Find the projection of the vector $ \vec{v_1} = \left(-9,~0,~2\right) $ on the vector $ \vec{v_2} = \left(1,~2,~-2\right) $. | 1 |
| 5411 | Find the projection of the vector $ \vec{v_1} = \left(-1,~0,~1\right) $ on the vector $ \vec{v_2} = \left(1,~4,~-4\right) $. | 1 |
| 5412 | Find the projection of the vector $ \vec{v_1} = \left(-4,~0,~1\right) $ on the vector $ \vec{v_2} = \left(1,~4,~-4\right) $. | 1 |
| 5413 | Find the projection of the vector $ \vec{v_1} = \left(-2,~2\right) $ on the vector $ \vec{v_2} = \left(3,~-1\right) $. | 1 |
| 5414 | Find the projection of the vector $ \vec{v_1} = \left(89,~157\right) $ on the vector $ \vec{v_2} = \left(237,~326\right) $. | 1 |
| 5415 | Determine whether the vectors $ \vec{v_1} = \left(89,~157\right) $ and $ \vec{v_2} = \left(237,~326\right) $ are linearly independent or dependent. | 1 |
| 5416 | Find the magnitude of the vector $ \| \vec{v} \| = \left(89,~157\right) $ . | 1 |
| 5417 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-3,~15\right) $ . | 1 |
| 5418 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-50,~4\right) $ . | 1 |
| 5419 | Find the difference of the vectors $ \vec{v_1} = \left(1,~-1\right) $ and $ \vec{v_2} = \left(-1,~-6\right) $ . | 1 |
| 5420 | Find the angle between vectors $ \left(1,~-1\right)$ and $\left(-1,~-6\right)$. | 1 |
| 5421 | Find the magnitude of the vector $ \| \vec{v} \| = \left(1,~0,~3\right) $ . | 1 |
| 5422 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~0,~3\right) $ and $ \vec{v_2} = \left(0,~1,~2\right) $ . | 1 |
| 5423 | Find the magnitude of the vector $ \| \vec{v} \| = \left(3,~0,~2\right) $ . | 1 |
| 5424 | Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~0,~2\right) $ and $ \vec{v_2} = \left(0,~3,~1\right) $ . | 1 |
| 5425 | Find the projection of the vector $ \vec{v_1} = \left(-1,~1,~2\right) $ on the vector $ \vec{v_2} = \left(-2,~8,~9\right) $. | 1 |
| 5426 | Find the angle between vectors $ \left(2,~-1\right)$ and $\left(-1,~4\right)$. | 1 |
| 5427 | Find the sum of the vectors $ \vec{v_1} = \left(3,~-1,~0\right) $ and $ \vec{v_2} = \left(2,~1,~3\right) $ . | 1 |
| 5428 | Find the angle between vectors $ \left(-3,~-1\right)$ and $\left(-9,~3\right)$. | 1 |
| 5429 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-6,~2\right) $ and $ \vec{v_2} = \left(-12,~36\right) $ . | 1 |
| 5430 | Calculate the dot product of the vectors $ \vec{v_1} = \left(6,~2\right) $ and $ \vec{v_2} = \left(-12,~36\right) $ . | 1 |
| 5431 | Determine whether the vectors $ \vec{v_1} = \left(4,~3\right) $ and $ \vec{v_2} = \left(-12,~16\right) $ are linearly independent or dependent. | 1 |
| 5432 | Calculate the cross product of the vectors $ \vec{v_1} = \left(3,~0,~1\right) $ and $ \vec{v_2} = \left(0,~1,~0\right) $ . | 1 |
| 5433 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-6,~-10,~-5\right) $ and $ \vec{v_2} = \left(-1,~-17,~-2\right) $ . | 1 |
| 5434 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-6,~-10,~-5\right) $ and $ \vec{v_2} = \left(-1,~-17,~-2\right) $ . | 1 |
| 5435 | Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~4,~0\right) $ and $ \vec{v_2} = \left(2,~1,~-4\right) $ . | 1 |
| 5436 | Calculate the cross product of the vectors $ \vec{v_1} = \left(0,~3,~-8\right) $ and $ \vec{v_2} = \left(2,~-2,~-3\right) $ . | 1 |
| 5437 | Find the angle between vectors $ \left(8,~-1,~2\right)$ and $\left(3,~1,~2\right)$. | 1 |
| 5438 | Find the angle between vectors $ \left(585,~-2,~0\right)$ and $\left(-3,~-3,~-2\right)$. | 1 |
| 5439 | Find the angle between vectors $ \left(5,~-2,~0\right)$ and $\left(-3,~-3,~-2\right)$. | 1 |
| 5440 | Calculate the cross product of the vectors $ \vec{v_1} = \left(4,~-4,~3\right) $ and $ \vec{v_2} = \left(3,~-1,~-3\right) $ . | 1 |
| 5441 | Calculate the cross product of the vectors $ \vec{v_1} = \left(2,~-1,~1\right) $ and $ \vec{v_2} = \left(3,~-1,~-3\right) $ . | 1 |
| 5442 | Find the sum of the vectors $ \vec{v_1} = \left(-5,~-5\right) $ and $ \vec{v_2} = \left(4,~2\right) $ . | 1 |
| 5443 | Find the sum of the vectors $ \vec{v_1} = \left(-2,~-10,~0\right) $ and $ \vec{v_2} = \left(10,~8,~0\right) $ . | 1 |
| 5444 | Find the angle between vectors $ \left(2,~2,~3\right)$ and $\left(-3,~5,~1\right)$. | 1 |
| 5445 | Find the angle between vectors $ \left(2,~2,~3\right)$ and $\left(-3,~5,~-1\right)$. | 1 |
| 5446 | Find the angle between vectors $ \left(-2,~-2,~-3\right)$ and $\left(-3,~5,~-1\right)$. | 1 |
| 5447 | Find the magnitude of the vector $ \| \vec{v} \| = \left(5,~3,~-5\right) $ . | 1 |
| 5448 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-5,~9\right) $ . | 1 |
| 5449 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-4,~-3,~-5\right) $ . | 1 |
| 5450 | Find the magnitude of the vector $ \| \vec{v} \| = \left(2,~0,~3\right) $ . | 1 |
