Vectors
(the database of solved problems)
All the problems and solutions shown below were generated using the Vectors Calculator.
| ID |
Problem |
Count |
| 4651 | Find the projection of the vector $ \vec{v_1} = \left(1,~2,~3\right) $ on the vector $ \vec{v_2} = \left(3,~-2,~1\right) $. | 1 |
| 4652 | Calculate the dot product of the vectors $ \vec{v_1} = \left(6,~2,~-5\right) $ and $ \vec{v_2} = \left(6,~3,~-7\right) $ . | 1 |
| 4653 | Find the angle between vectors $ \left(6,~2,~-5\right)$ and $\left(6,~3,~-7\right)$. | 1 |
| 4654 | Find the angle between vectors $ \left(-9,~7\right)$ and $\left(-9,~-4\right)$. | 1 |
| 4655 | Find the angle between vectors $ \left(-8,~-6\right)$ and $\left(9,~-8\right)$. | 1 |
| 4656 | Find the angle between vectors $ \left(9,~-4\right)$ and $\left(8,~7\right)$. | 1 |
| 4657 | Find the angle between vectors $ \left(8,~4\right)$ and $\left(-9,~1\right)$. | 1 |
| 4658 | Find the angle between vectors $ \left(-5,~-4\right)$ and $\left(-6,~5\right)$. | 1 |
| 4659 | Find the angle between vectors $ \left(5,~1\right)$ and $\left(1,~-5\right)$. | 1 |
| 4660 | Find the angle between vectors $ \left(4,~-1\right)$ and $\left(-8,~2\right)$. | 1 |
| 4661 | Find the angle between vectors $ \left(5,~-2\right)$ and $\left(9,~7\right)$. | 1 |
| 4662 | Find the angle between vectors $ \left(-7,~5\right)$ and $\left(7,~4\right)$. | 1 |
| 4663 | Find the angle between vectors $ \left(-5,~1\right)$ and $\left(-1,~-5\right)$. | 1 |
| 4664 | Calculate the cross product of the vectors $ \vec{v_1} = \left(2,~-2,~2\right) $ and $ \vec{v_2} = \left(5,~5,~-5\right) $ . | 1 |
| 4665 | Calculate the cross product of the vectors $ \vec{v_1} = \left(3,~2,~0\right) $ and $ \vec{v_2} = \left(1,~0,~1\right) $ . | 1 |
| 4666 | Calculate the cross product of the vectors $ \vec{v_1} = \left(3,~4,~0\right) $ and $ \vec{v_2} = \left(2,~1,~3\right) $ . | 1 |
| 4667 | Calculate the cross product of the vectors $ \vec{v_1} = \left(3,~4,~0\right) $ and $ \vec{v_2} = \left(2,~-1,~3\right) $ . | 1 |
| 4668 | Find the magnitude of the vector $ \| \vec{v} \| = \left(12,~-9,~-11\right) $ . | 1 |
| 4669 | Find the sum of the vectors $ \vec{v_1} = \left(1,~2,~3\right) $ and $ \vec{v_2} = \left(0,~1,~1\right) $ . | 1 |
| 4670 | Find the angle between vectors $ \left(2,~1,~-3\right)$ and $\left(3,~-2,~1\right)$. | 1 |
| 4671 | Find the magnitude of the vector $ \| \vec{v} \| = \left(0,~4,~1\right) $ . | 1 |
| 4672 | Find the magnitude of the vector $ \| \vec{v} \| = \left(3,~1,~-2\right) $ . | 1 |
| 4673 | Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~2,~1\right) $ and $ \vec{v_2} = \left(2,~-5,~3\right) $ . | 1 |
| 4674 | Find the angle between vectors $ \left(2,~2,~-4\right)$ and $\left(1,~0,~0\right)$. | 1 |
| 4675 | Find the magnitude of the vector $ \| \vec{v} \| = \left(7,~-2,~-4\right) $ . | 1 |
| 4676 | Find the angle between vectors $ \left(1,~2,~3\right)$ and $\left(7,~-2,~-4\right)$. | 1 |
| 4677 | Find the sum of the vectors $ \vec{v_1} = \left(1,~2,~3\right) $ and $ \vec{v_2} = \left(7,~-2,~-4\right) $ . | 1 |
| 4678 | Find the difference of the vectors $ \vec{v_1} = \left(1,~2,~3\right) $ and $ \vec{v_2} = \left(7,~-2,~-4\right) $ . | 1 |
| 4679 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~2,~3\right) $ and $ \vec{v_2} = \left(7,~-2,~-4\right) $ . | 1 |
| 4680 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-10,~-10,~20\right) $ and $ \vec{v_2} = \left(1,~-1,~0\right) $ . | 1 |
| 4681 | Find the angle between vectors $ \left(2,~2,~-4\right)$ and $\left(-10,~-10,~20\right)$. | 1 |
| 4682 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-2,~2,~-1\right) $ . | 1 |
| 4683 | Find the projection of the vector $ \vec{v_1} = \left(-2,~2,~-1\right) $ on the vector $ \vec{v_2} = \left(0,~3,~-3\right) $. | 1 |
| 4684 | Determine whether the vectors $ \vec{v_1} = \left(-2,~2,~-1\right) $, $ \vec{v_2} = \left(0,~3,~-3\right) $ and $ \vec{v_3} = \left(0,~0,~-4\right)$ are linearly independent or dependent. | 1 |
| 4685 | Find the angle between vectors $ \left(4,~5,~-2\right)$ and $\left(3,~-1,~5\right)$. | 1 |
| 4686 | Find the angle between vectors $ \left(-8,~12,~4\right)$ and $\left(6,~-9,~-3\right)$. | 1 |
| 4687 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-2,~0\right) $ . | 1 |
| 4688 | Find the magnitude of the vector $ \| \vec{v} \| = \left(3,~8\right) $ . | 1 |
| 4689 | Find the angle between vectors $ \left(1,~-3,~-2\right)$ and $\left(2,~0,~-4\right)$. | 1 |
| 4690 | Find the angle between vectors $ \left(6,~-2,~-5\right)$ and $\left(2,~0,~-4\right)$. | 1 |
| 4691 | Find the angle between vectors $ \left(6,~-2,~-5\right)$ and $\left(1,~-3,~-2\right)$. | 1 |
| 4692 | Find the angle between vectors $ \left(1,~1,~0\right)$ and $\left(-1,~1,~1\right)$. | 1 |
| 4693 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~1,~0\right) $ and $ \vec{v_2} = \left(-1,~1,~1\right) $ . | 1 |
| 4694 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~0,~1\right) $ and $ \vec{v_2} = \left(-1,~1,~1\right) $ . | 1 |
| 4695 | Find the sum of the vectors $ \vec{v_1} = \left(24,~12,~16 \sqrt{ 5 }\right) $ and $ \vec{v_2} = \left(9,~0,~15 \sqrt{ 5 }\right) $ . | 1 |
| 4696 | Find the difference of the vectors $ \vec{v_1} = \left(12,~6,~8 \sqrt{ 5 }\right) $ and $ \vec{v_2} = \left(3,~0,~5 \sqrt{ 5 }\right) $ . | 1 |
| 4697 | Calculate the dot product of the vectors $ \vec{v_1} = \left(5,~-1\right) $ and $ \vec{v_2} = \left(-1,~5\right) $ . | 1 |
| 4698 | Find the magnitude of the vector $ \| \vec{v} \| = \left(5,~-1\right) $ . | 1 |
| 4699 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-3,~4\right) $ and $ \vec{v_2} = \left(-1,~1\right) $ . | 1 |
| 4700 | Calculate the cross product of the vectors $ \vec{v_1} = \left(2,~0,~2\right) $ and $ \vec{v_2} = \left(2,~2 \sqrt{ 2 },~2\right) $ . | 1 |
