Vectors
(the database of solved problems)
All the problems and solutions shown below were generated using the Vectors Calculator.
| ID |
Problem |
Count |
| 3551 | Find the projection of the vector $ \vec{v_1} = \left(-2,~3,~8\right) $ on the vector $ \vec{v_2} = \left(-3,~1,~5\right) $. | 1 |
| 3552 | Find the magnitude of the vector $ \| \vec{v} \| = \left(7,~190\right) $ . | 1 |
| 3553 | Find the angle between vectors $ \left(1,~2,~3\right)$ and $\left(1,~2,~0\right)$. | 1 |
| 3554 | Find the magnitude of the vector $ \| \vec{v} \| = \left(1,~3,~-2\right) $ . | 1 |
| 3555 | Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~17,~-11\right) $ and $ \vec{v_2} = \left(3,~0,~4\right) $ . | 1 |
| 3556 | Calculate the cross product of the vectors $ \vec{v_1} = \left(5,~7,~1\right) $ and $ \vec{v_2} = \left(4,~0,~2\right) $ . | 1 |
| 3557 | Find the angle between vectors $ \left(3,~7,~1\right)$ and $\left(6,~0,~2\right)$. | 1 |
| 3558 | Find the magnitude of the vector $ \| \vec{v} \| = \left(2,~3,~-2\right) $ . | 1 |
| 3559 | Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~11,~-11\right) $ and $ \vec{v_2} = \left(2,~0,~6\right) $ . | 1 |
| 3560 | Calculate the cross product of the vectors $ \vec{v_1} = \left(2,~7,~1\right) $ and $ \vec{v_2} = \left(4,~0,~1\right) $ . | 1 |
| 3561 | Find the angle between vectors $ \left(5,~7,~1\right)$ and $\left(6,~0,~1\right)$. | 1 |
| 3562 | Find the magnitude of the vector $ \| \vec{v} \| = \left(1,~0,~0\right) $ . | 1 |
| 3563 | Find the sum of the vectors $ \vec{v_1} = \left(1,~0,~0\right) $ and $ \vec{v_2} = \left(-\dfrac{ 1 }{ 2 },~\dfrac{\sqrt{ 3 }}{ 2 },~0\right) $ . | 1 |
| 3564 | Find the magnitude of the vector $ \| \vec{v} \| = \left(1,~2,~-2\right) $ . | 1 |
| 3565 | Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~-13,~-5\right) $ and $ \vec{v_2} = \left(5,~0,~2\right) $ . | 1 |
| 3566 | Calculate the cross product of the vectors $ \vec{v_1} = \left(3,~7,~1\right) $ and $ \vec{v_2} = \left(4,~0,~1\right) $ . | 1 |
| 3567 | Find the angle between vectors $ \left(3,~7,~1\right)$ and $\left(6,~0,~1\right)$. | 1 |
| 3568 | Determine whether the vectors $ \vec{v_1} = \left(4,~4,~2\right) $, $ \vec{v_2} = \left(-8,~6,~1\right) $ and $ \vec{v_3} = \left(-8,~-2,~1\right)$ are linearly independent or dependent. | 1 |
| 3569 | Calculate the dot product of the vectors $ \vec{v_1} = \left(4,~2,~1\right) $ and $ \vec{v_2} = \left(1,~3,~2\right) $ . | 1 |
| 3570 | Find the magnitude of the vector $ \| \vec{v} \| = \left(2,~1\right) $ . | 1 |
| 3571 | Find the angle between vectors $ \left(2,~1\right)$ and $\left(5,~4\right)$. | 1 |
| 3572 | Find the projection of the vector $ \vec{v_1} = \left(1,~0,~3\right) $ on the vector $ \vec{v_2} = \left(3,~-1,~2\right) $. | 1 |
| 3573 | Find the magnitude of the vector $ \| \vec{v} \| = \left(1,~0,~3\right) $ . | 1 |
| 3574 | Calculate the cross product of the vectors $ \vec{v_1} = \left(2,~0,~-6\right) $ and $ \vec{v_2} = \left(7,~6,~2\right) $ . | 1 |
| 3575 | Calculate the dot product of the vectors $ \vec{v_1} = \left(36,~-46,~12\right) $ and $ \vec{v_2} = \left(-3,~5,~9\right) $ . | 1 |
| 3576 | Calculate the cross product of the vectors $ \vec{v_1} = \left(2,~2,~3\right) $ and $ \vec{v_2} = \left(2,~3,~4\right) $ . | 1 |
| 3577 | Find the magnitude of the vector $ \| \vec{v} \| = \left(0,~0\right) $ . | 1 |
| 3578 | Find the sum of the vectors $ \vec{v_1} = \left(5,~9\right) $ and $ \vec{v_2} = \left(-2,~4\right) $ . | 1 |
| 3579 | Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~2,~6\right) $ and $ \vec{v_2} = \left(2,~2,~6\right) $ . | 1 |
| 3580 | Calculate the cross product of the vectors $ \vec{v_1} = \left(2,~2,~6\right) $ and $ \vec{v_2} = \left(2,~2,~6\right) $ . | 1 |
| 3581 | Find the magnitude of the vector $ \| \vec{v} \| = \left(2,~2,~6\right) $ . | 1 |
| 3582 | Find the magnitude of the vector $ \| \vec{v} \| = \left(6,~9,~-8\right) $ . | 1 |
| 3583 | Find the projection of the vector $ \vec{v_1} = \left(3,~-3\right) $ on the vector $ \vec{v_2} = \left(4,~9\right) $. | 1 |
| 3584 | Calculate the cross product of the vectors $ \vec{v_1} = \left(4,~0,~3\right) $ and $ \vec{v_2} = \left(0,~-2,~-5\right) $ . | 1 |
| 3585 | Find the sum of the vectors $ \vec{v_1} = \left(24,~6\right) $ and $ \vec{v_2} = \left(-42,~56\right) $ . | 1 |
| 3586 | Calculate the dot product of the vectors $ \vec{v_1} = \left(32,~8\right) $ and $ \vec{v_2} = \left(18,~-24\right) $ . | 1 |
| 3587 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~3,~5\right) $ and $ \vec{v_2} = \left(1,~3,~5\right) $ . | 1 |
| 3588 | Find the magnitude of the vector $ \| \vec{v} \| = \left(1,~3,~5\right) $ . | 1 |
| 3589 | Find the magnitude of the vector $ \| \vec{v} \| = \left(3,~-1,~-3\right) $ . | 1 |
| 3590 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-1,~-3,~2\right) $ and $ \vec{v_2} = \left(4,~-2,~-1\right) $ . | 1 |
| 3591 | Find the sum of the vectors $ \vec{v_1} = \left(6,~7\right) $ and $ \vec{v_2} = \left(-3,~-1\right) $ . | 1 |
| 3592 | Find the sum of the vectors $ \vec{v_1} = \left(-2,~-8\right) $ and $ \vec{v_2} = \left(5,~5\right) $ . | 1 |
| 3593 | Determine whether the vectors $ \vec{v_1} = \left(6,~4\right) $ and $ \vec{v_2} = \left(6,~0\right) $ are linearly independent or dependent. | 1 |
| 3594 | Find the projection of the vector $ \vec{v_1} = \left(6,~4\right) $ on the vector $ \vec{v_2} = \left(6,~0\right) $. | 1 |
| 3595 | Find the sum of the vectors $ \vec{v_1} = \left(6,~4\right) $ and $ \vec{v_2} = \left(6,~0\right) $ . | 1 |
| 3596 | Find the difference of the vectors $ \vec{v_1} = \left(6,~4\right) $ and $ \vec{v_2} = \left(6,~0\right) $ . | 1 |
| 3597 | Find the magnitude of the vector $ \| \vec{v} \| = \left(0,~5\right) $ . | 1 |
| 3598 | Find the difference of the vectors $ \vec{v_1} = \left(3,~-1\right) $ and $ \vec{v_2} = \left(0,~5\right) $ . | 1 |
| 3599 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-6,~-6\right) $ . | 1 |
| 3600 | Find the magnitude of the vector $ \| \vec{v} \| = \left(2,~-6\right) $ . | 1 |
