Vectors
(the database of solved problems)
All the problems and solutions shown below were generated using the Vectors Calculator.
| ID |
Problem |
Count |
| 5601 | Calculate the dot product of the vectors $ \vec{v_1} = \left(0,~0,~3\right) $ and $ \vec{v_2} = \left(7,~0,~0\right) $ . | 1 |
| 5602 | Find the difference of the vectors $ \vec{v_1} = \left(-3,~4\right) $ and $ \vec{v_2} = \left(-2,~5\right) $ . | 1 |
| 5603 | Find the sum of the vectors $ \vec{v_1} = \left(4,~4,~11\right) $ and $ \vec{v_2} = \left(7,~-2,~2\right) $ . | 1 |
| 5604 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-1,~2\right) $ and $ \vec{v_2} = \left(1,~1\right) $ . | 1 |
| 5605 | Calculate the cross product of the vectors $ \vec{v_1} = \left(2,~-1,~-6\right) $ and $ \vec{v_2} = \left(1,~2,~3\right) $ . | 1 |
| 5606 | Calculate the cross product of the vectors $ \vec{v_1} = \left(5,~0,~0\right) $ and $ \vec{v_2} = \left(\dfrac{ 3 }{ 5 },~0,~0\right) $ . | 1 |
| 5607 | Find the difference of the vectors $ \vec{v_1} = \left(8,~-20\right) $ and $ \vec{v_2} = \left(0,~-16\right) $ . | 1 |
| 5608 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-1,~2,~2\right) $ and $ \vec{v_2} = \left(-1,~7,~2\right) $ . | 1 |
| 5609 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-1,~2,~2\right) $ and $ \vec{v_2} = \left(-1,~7,~2\right) $ . | 1 |
| 5610 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-2,~0,~0\right) $ . | 1 |
| 5611 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-5,~6\right) $ and $ \vec{v_2} = \left(-2,~-3\right) $ . | 1 |
| 5612 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-4,~-6\right) $ . | 1 |
| 5613 | Find the magnitude of the vector $ \| \vec{v} \| = \left(40,~21,~60\right) $ . | 1 |
| 5614 | Find the magnitude of the vector $ \| \vec{v} \| = \left(3,~-4,~4\right) $ . | 1 |
| 5615 | Find the angle between vectors $ \left(3,~-4,~4\right)$ and $\left(2,~3,~-7\right)$. | 1 |
| 5616 | Calculate the dot product of the vectors $ \vec{v_1} = \left(0,~0,~1\right) $ and $ \vec{v_2} = \left(0,~0,~0\right) $ . | 1 |
| 5617 | Find the magnitude of the vector $ \| \vec{v} \| = \left(2,~10\right) $ . | 1 |
| 5618 | Find the angle between vectors $ \left(2,~6\right)$ and $\left(-6,~2\right)$. | 1 |
| 5619 | Find the angle between vectors $ \left(2,~-2\right)$ and $\left(2,~2\right)$. | 1 |
| 5620 | Find the angle between vectors $ \left(2,~-\dfrac{ 4001 }{ 1000 }\right)$ and $\left(4,~2\right)$. | 1 |
| 5621 | Find the angle between vectors $ \left(2,~-\dfrac{ 3999 }{ 1000 }\right)$ and $\left(4,~2\right)$. | 1 |
| 5622 | Find the angle between vectors $ \left(2,~4\right)$ and $\left(4,~2\right)$. | 1 |
| 5623 | Find the angle between vectors $ \left(2,~5\right)$ and $\left(4,~2\right)$. | 1 |
| 5624 | Find the angle between vectors $ \left(2,~-19\right)$ and $\left(20,~2\right)$. | 1 |
| 5625 | Find the angle between vectors $ \left(2,~-20\right)$ and $\left(19,~40\right)$. | 1 |
| 5626 | Find the angle between vectors $ \left(2,~-18\right)$ and $\left(19,~40\right)$. | 1 |
| 5627 | Find the angle between vectors $ \left(15,~-18\right)$ and $\left(19,~40\right)$. | 1 |
| 5628 | Find the angle between vectors $ \left(1,~-1\right)$ and $\left(1,~1\right)$. | 1 |
| 5629 | Find the angle between vectors $ \left(2,~-1\right)$ and $\left(1,~1\right)$. | 1 |
| 5630 | Find the angle between vectors $ \left(1,~-1\right)$ and $\left(1,~2\right)$. | 1 |
| 5631 | Find the angle between vectors $ \left(\dfrac{ 1 }{ 4 },~-1\right)$ and $\left(\dfrac{ 1 }{ 4 },~1\right)$. | 1 |
| 5632 | Find the angle between vectors $ \left(7,~-5\right)$ and $\left(4,~1\right)$. | 1 |
| 5633 | Find the angle between vectors $ \left(5,~-5\right)$ and $\left(5,~\dfrac{ 501 }{ 100 }\right)$. | 1 |
| 5634 | Find the angle between vectors $ \left(5,~-5\right)$ and $\left(\dfrac{ 501 }{ 100 },~5\right)$. | 1 |
| 5635 | Find the angle between vectors $ \left(1,~-2\right)$ and $\left(3,~1\right)$. | 1 |
| 5636 | Find the angle between vectors $ \left(4,~4\right)$ and $\left(-4,~-4\right)$. | 1 |
| 5637 | Find the angle between vectors $ \left(4,~-4\right)$ and $\left(-4,~-4\right)$. | 1 |
| 5638 | Find the angle between vectors $ \left(4,~4\right)$ and $\left(4,~4\right)$. | 1 |
| 5639 | Find the angle between vectors $ \left(-4,~4\right)$ and $\left(-4,~4\right)$. | 1 |
| 5640 | Find the angle between vectors $ \left(-4,~-4\right)$ and $\left(-4,~4\right)$. | 1 |
| 5641 | Calculate the dot product of the vectors $ \vec{v_1} = \left(4,~10,~4\right) $ and $ \vec{v_2} = \left(0,~12,~2\right) $ . | 1 |
| 5642 | Find the magnitude of the vector $ \| \vec{v} \| = \left(3,~-1\right) $ . | 1 |
| 5643 | Find the angle between vectors $ \left(3,~-1\right)$ and $\left(2,~7\right)$. | 1 |
| 5644 | Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~-1,~2\right) $ and $ \vec{v_2} = \left(1,~0,~2\right) $ . | 1 |
| 5645 | Find the magnitude of the vector $ \| \vec{v} \| = \left(2,~-1,~2\right) $ . | 1 |
| 5646 | Determine whether the vectors $ \vec{v_1} = \left(2,~-1,~2\right) $, $ \vec{v_2} = \left(1,~0,~2\right) $ and $ \vec{v_3} = \left(3,~-1,~1\right)$ are linearly independent or dependent. | 1 |
| 5647 | Find the projection of the vector $ \vec{v_1} = \left(2,~-1,~2\right) $ on the vector $ \vec{v_2} = \left(1,~0,~2\right) $. | 1 |
| 5648 | Determine whether the vectors $ \vec{v_1} = \left(25,~64,~144\right) $, $ \vec{v_2} = \left(5,~8,~12\right) $ and $ \vec{v_3} = \left(1,~1,~1\right)$ are linearly independent or dependent. | 1 |
| 5649 | Determine whether the vectors $ \vec{v_1} = \left(1,~2,~6\right) $, $ \vec{v_2} = \left(2,~5,~14\right) $ and $ \vec{v_3} = \left(5,~7,~24\right)$ are linearly independent or dependent. | 1 |
| 5650 | Find the sum of the vectors $ \vec{v_1} = \left(-2,~-4\right) $ and $ \vec{v_2} = \left(1,~3\right) $ . | 1 |
