Vectors
(the database of solved problems)
All the problems and solutions shown below were generated using the Vectors Calculator.
| ID |
Problem |
Count |
| 3601 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-3,~-4\right) $ . | 1 |
| 3602 | Find the difference of the vectors $ \vec{v_1} = \left(-3,~-4\right) $ and $ \vec{v_2} = \left(6,~-16\right) $ . | 1 |
| 3603 | Determine whether the vectors $ \vec{v_1} = \left(-3,~-4\right) $ and $ \vec{v_2} = \left(6,~-16\right) $ are linearly independent or dependent. | 1 |
| 3604 | Find the magnitude of the vector $ \| \vec{v} \| = \left(2,~2\right) $ . | 1 |
| 3605 | Find the sum of the vectors $ \vec{v_1} = \left(-5,~-3\right) $ and $ \vec{v_2} = \left(5,~2\right) $ . | 1 |
| 3606 | Find the difference of the vectors $ \vec{v_1} = \left(-2,~7,~-7\right) $ and $ \vec{v_2} = \left(-\dfrac{ 174 }{ 61 },~\dfrac{ 348 }{ 61 },~\dfrac{ 232 }{ 61 }\right) $ . | 1 |
| 3607 | Find the magnitude of the vector $ \| \vec{v} \| = \left(2,~5\right) $ . | 1 |
| 3608 | Find the magnitude of the vector $ \| \vec{v} \| = \left(4,~7\right) $ . | 1 |
| 3609 | Find the angle between vectors $ \left(-\dfrac{ 61 }{ 10 },~\dfrac{ 17 }{ 2 }\right)$ and $\left(-5,~\dfrac{ 9 }{ 2 }\right)$. | 1 |
| 3610 | Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~4\right) $ and $ \vec{v_2} = \left(-1,~5\right) $ . | 1 |
| 3611 | Find the angle between vectors $ \left(-2,~5\right)$ and $\left(4,~-3\right)$. | 1 |
| 3612 | Calculate the dot product of the vectors $ \vec{v_1} = \left(\dfrac{ 46 }{ 17 },~\dfrac{ 80 }{ 17 }\right) $ and $ \vec{v_2} = \left(4,~1\right) $ . | 1 |
| 3613 | Find the angle between vectors $ \left(-\dfrac{ 20 }{ 17 },~\dfrac{ 80 }{ 17 }\right)$ and $\left(4,~1\right)$. | 1 |
| 3614 | Find the difference of the vectors $ \vec{v_1} = \left(2,~-3\right) $ and $ \vec{v_2} = \left(1,~0\right) $ . | 1 |
| 3615 | Find the sum of the vectors $ \vec{v_1} = \left(-1,~3\right) $ and $ \vec{v_2} = \left(-1,~-2\right) $ . | 1 |
| 3616 | Find the difference of the vectors $ \vec{v_1} = \left(-1,~3\right) $ and $ \vec{v_2} = \left(-1,~-2\right) $ . | 1 |
| 3617 | Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~6\right) $ and $ \vec{v_2} = \left(3,~-7\right) $ . | 1 |
| 3618 | Calculate the dot product of the vectors $ \vec{v_1} = \left(7,~-2\right) $ and $ \vec{v_2} = \left(-8,~-2\right) $ . | 1 |
| 3619 | Find the sum of the vectors $ \vec{v_1} = \left(6,~9\right) $ and $ \vec{v_2} = \left(6,~9\right) $ . | 1 |
| 3620 | Calculate the dot product of the vectors $ \vec{v_1} = \left(\sqrt{ 7 },~\sqrt{ 8 }\right) $ and $ \vec{v_2} = \left(\sqrt{ 8 },~-\sqrt{ 7 }\right) $ . | 1 |
| 3621 | Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~-3\right) $ and $ \vec{v_2} = \left(3,~-3\right) $ . | 1 |
| 3622 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-1,~5,~6\right) $ and $ \vec{v_2} = \left(-3,~5,~6\right) $ . | 1 |
| 3623 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-9,~7,~5\right) $ and $ \vec{v_2} = \left(9,~3,~2\right) $ . | 1 |
| 3624 | Find the angle between vectors $ \left(-9,~7,~5\right)$ and $\left(9,~3,~2\right)$. | 1 |
| 3625 | Find the projection of the vector $ \vec{v_1} = \left(6,~3,~5\right) $ on the vector $ \vec{v_2} = \left(-5,~8,~3\right) $. | 1 |
| 3626 | Find the sum of the vectors $ \vec{v_1} = \left(10,~0\right) $ and $ \vec{v_2} = \left(-14.3,~-2.34\right) $ . | 1 |
| 3627 | Calculate the cross product of the vectors $ \vec{v_1} = \left(23,~6,~0\right) $ and $ \vec{v_2} = \left(17,~5,~0\right) $ . | 1 |
| 3628 | Find the angle between vectors $ \left(5,~5,~1\right)$ and $\left(-1,~-2,~-1\right)$. | 1 |
| 3629 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-2,~-1,~5\right) $ . | 1 |
| 3630 | Find the difference of the vectors $ \vec{v_1} = \left(-2,~-1,~5\right) $ and $ \vec{v_2} = \left(-1,~-4,~3\right) $ . | 1 |
| 3631 | Find the sum of the vectors $ \vec{v_1} = \left(-2,~-1,~5\right) $ and $ \vec{v_2} = \left(-1,~-4,~3\right) $ . | 1 |
| 3632 | Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~1\right) $ and $ \vec{v_2} = \left(-2,~1\right) $ . | 1 |
| 3633 | Find the angle between vectors $ \left(3,~1\right)$ and $\left(-2,~1\right)$. | 1 |
| 3634 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~2,~1\right) $ and $ \vec{v_2} = \left(2,~2,~0\right) $ . | 1 |
| 3635 | Find the magnitude of the vector $ \| \vec{v} \| = \left(2,~2,~2\right) $ . | 1 |
| 3636 | Find the magnitude of the vector $ \| \vec{v} \| = \left(4,~5,~2\right) $ . | 1 |
| 3637 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~-4,~1\right) $ and $ \vec{v_2} = \left(4,~-1,~-5\right) $ . | 1 |
| 3638 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-4,~2,~2\right) $ and $ \vec{v_2} = \left(2,~-3,~1\right) $ . | 1 |
| 3639 | Determine whether the vectors $ \vec{v_1} = \left(-4,~2,~2\right) $, $ \vec{v_2} = \left(2,~-3,~1\right) $ and $ \vec{v_3} = \left(1,~-1,~2\right)$ are linearly independent or dependent. | 1 |
| 3640 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-1,~2,~3\right) $ and $ \vec{v_2} = \left(2,~1,~4\right) $ . | 1 |
| 3641 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-1,~2,~3\right) $ and $ \vec{v_2} = \left(2,~1,~4\right) $ . | 1 |
| 3642 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-1,~2,~3\right) $ and $ \vec{v_2} = \left(0,~5,~-1\right) $ . | 1 |
| 3643 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~2,~-3\right) $ and $ \vec{v_2} = \left(-2,~-2,~4\right) $ . | 1 |
| 3644 | Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~3,~1\right) $ and $ \vec{v_2} = \left(3,~1,~-1\right) $ . | 1 |
| 3645 | Calculate the cross product of the vectors $ \vec{v_1} = \left(2,~3,~1\right) $ and $ \vec{v_2} = \left(3,~1,~-1\right) $ . | 1 |
| 3646 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-3,~2\right) $ . | 1 |
| 3647 | Find the sum of the vectors $ \vec{v_1} = \left(2,~-1,~3\right) $ and $ \vec{v_2} = \left(2,~0,~2\right) $ . | 1 |
| 3648 | Find the sum of the vectors $ \vec{v_1} = \left(2,~-1,~3\right) $ and $ \vec{v_2} = \left(3,~0,~3\right) $ . | 1 |
| 3649 | Find the difference of the vectors $ \vec{v_1} = \left(2,~-1,~3\right) $ and $ \vec{v_2} = \left(3,~0,~3\right) $ . | 1 |
| 3650 | Calculate the dot product of the vectors $ \vec{v_1} = \left(4,~-1,~5\right) $ and $ \vec{v_2} = \left(-1,~-1,~0\right) $ . | 1 |
