Vectors
(the database of solved problems)
All the problems and solutions shown below were generated using the Vectors Calculator.
| ID |
Problem |
Count |
| 4551 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-5,~-1,~5\right) $ and $ \vec{v_2} = \left(3,~1,~2\right) $ . | 1 |
| 4552 | Find the angle between vectors $ \left(3,~5\right)$ and $\left(4,~-3\right)$. | 1 |
| 4553 | Calculate the cross product of the vectors $ \vec{v_1} = \left(0,~2,~-5\right) $ and $ \vec{v_2} = \left(-4,~9,~0\right) $ . | 1 |
| 4554 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-5,~2,~1\right) $ . | 1 |
| 4555 | Calculate the dot product of the vectors $ \vec{v_1} = \left(12,~10,~-3\right) $ and $ \vec{v_2} = \left(5,~2,~2\right) $ . | 1 |
| 4556 | Calculate the dot product of the vectors $ \vec{v_1} = \left(12,~-10,~-3\right) $ and $ \vec{v_2} = \left(5,~2,~2\right) $ . | 1 |
| 4557 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-12,~10,~-3\right) $ and $ \vec{v_2} = \left(5,~2,~2\right) $ . | 1 |
| 4558 | Find the sum of the vectors $ \vec{v_1} = \left(3,~-2\right) $ and $ \vec{v_2} = \left(-1,~5\right) $ . | 1 |
| 4559 | Find the sum of the vectors $ \vec{v_1} = \left(2,~-1,~0\right) $ and $ \vec{v_2} = \left(0,~-3,~0\right) $ . | 1 |
| 4560 | Determine whether the vectors $ \vec{v_1} = \left(1,~1,~-2\right) $, $ \vec{v_2} = \left(-2,~1,~1\right) $ and $ \vec{v_3} = \left(1,~-1,~0\right)$ are linearly independent or dependent. | 1 |
| 4561 | Find the angle between vectors $ \left(-3,~4,~-5\right)$ and $\left(3,~4,~5\right)$. | 1 |
| 4562 | Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~1,~1\right) $ and $ \vec{v_2} = \left(1,~-1,~2\right) $ . | 1 |
| 4563 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~-1,~2\right) $ and $ \vec{v_2} = \left(2,~1,~5\right) $ . | 1 |
| 4564 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~-1,~2\right) $ and $ \vec{v_2} = \left(2,~1,~5\right) $ . | 1 |
| 4565 | Calculate the dot product of the vectors $ \vec{v_1} = \left(11,~2,~-10\right) $ and $ \vec{v_2} = \left(8,~15,~0\right) $ . | 1 |
| 4566 | Find the angle between vectors $ \left(1,~0,~-3\right)$ and $\left(0,~0,~-6\right)$. | 1 |
| 4567 | Find the angle between vectors $ \left(1,~0,~-3\right)$ and $\left(3,~0,~-6\right)$. | 1 |
| 4568 | Find the angle between vectors $ \left(1,~0,~-3\right)$ and $\left(-1,~0,~3\right)$. | 1 |
| 4569 | Find the angle between vectors $ \left(1,~0,~-3\right)$ and $\left(2,~0,~-2\right)$. | 1 |
| 4570 | Find the angle between vectors $ \left(1,~0,~-3\right)$ and $\left(4,~0,~-12\right)$. | 1 |
| 4571 | Find the angle between vectors $ \left(1,~0,~-3\right)$ and $\left(0,~-3,~1\right)$. | 1 |
| 4572 | Find the sum of the vectors $ \vec{v_1} = \left(56,~14\right) $ and $ \vec{v_2} = \left(20,~25\right) $ . | 1 |
| 4573 | Find the difference of the vectors $ \vec{v_1} = \left(7,~-4\right) $ and $ \vec{v_2} = \left(4,~8\right) $ . | 1 |
| 4574 | Find the difference of the vectors $ \vec{v_1} = \left(3,~2\right) $ and $ \vec{v_2} = \left(7,~-4\right) $ . | 1 |
| 4575 | Find the magnitude of the vector $ \| \vec{v} \| = \left(3,~-12\right) $ . | 1 |
| 4576 | Find the magnitude of the vector $ \| \vec{v} \| = \left(24,~10\right) $ . | 1 |
| 4577 | Find the sum of the vectors $ \vec{v_1} = \left(12,~3,~18 \sqrt{ 3 }\right) $ and $ \vec{v_2} = \left(4,~0,~36 \sqrt{ 3 }\right) $ . | 1 |
| 4578 | Find the difference of the vectors $ \vec{v_1} = \left(8,~2,~12 \sqrt{ 3 }\right) $ and $ \vec{v_2} = \left(1,~0,~9 \sqrt{ 3 }\right) $ . | 1 |
| 4579 | Find the sum of the vectors $ \vec{v_1} = \left(4,~1,~6 \sqrt{ 3 }\right) $ and $ \vec{v_2} = \left(2,~0,~18 \sqrt{ 3 }\right) $ . | 1 |
| 4580 | Find the magnitude of the vector $ \| \vec{v} \| = \left(6,~1,~24 \sqrt{ 3 }\right) $ . | 1 |
| 4581 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-4,~5\right) $ and $ \vec{v_2} = \left(-1,~1\right) $ . | 1 |
| 4582 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-1,~1\right) $ . | 1 |
| 4583 | Find the magnitude of the vector $ \| \vec{v} \| = \left(\dfrac{ 3 }{ 125 },~-\dfrac{ 3 }{ 500 },~0\right) $ . | 1 |
| 4584 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~3,~4\right) $ and $ \vec{v_2} = \left(1,~-3,~2\right) $ . | 1 |
| 4585 | Calculate the dot product of the vectors $ \vec{v_1} = \left(9,~8,~-17\right) $ and $ \vec{v_2} = \left(1,~-6,~-1\right) $ . | 1 |
| 4586 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-2,~2,~-2\right) $ and $ \vec{v_2} = \left(3,~2,~1\right) $ . | 1 |
| 4587 | Find the difference of the vectors $ \vec{v_1} = \left(\dfrac{ 26997 }{ 200 },~-\dfrac{ 160869 }{ 1000 }\right) $ and $ \vec{v_2} = \left(-\dfrac{ 64279 }{ 5000 },~-\dfrac{ 153209 }{ 10000 }\right) $ . | 1 |
| 4588 | Find the difference of the vectors $ \vec{v_1} = \left(230,~75\right) $ and $ \vec{v_2} = \left(-190,~30\right) $ . | 1 |
| 4589 | Find the magnitude of the vector $ \| \vec{v} \| = \left(\dfrac{ 73 }{ 1000 },~0,~0\right) $ . | 1 |
| 4590 | Find the angle between vectors $ \left(1,~3,~-2\right)$ and $\left(-9,~1,~-5\right)$. | 1 |
| 4591 | Find the magnitude of the vector $ \| \vec{v} \| = \left(2,~-4,~1\right) $ . | 1 |
| 4592 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~0,~-3\right) $ and $ \vec{v_2} = \left(-2,~5,~1\right) $ . | 1 |
| 4593 | Find the angle between vectors $ \left(-1,~-1,~1\right)$ and $\left(-1,~-1,~2\right)$. | 1 |
| 4594 | Find the angle between vectors $ \left(2,~-1,~1\right)$ and $\left(2,~2,~-2\right)$. | 1 |
| 4595 | Find the magnitude of the vector $ \| \vec{v} \| = \left(4,~5\right) $ . | 1 |
| 4596 | Find the magnitude of the vector $ \| \vec{v} \| = \left(1,~0,~0\right) $ . | 1 |
| 4597 | Find the angle between vectors $ \left(4,~6,~-3\right)$ and $\left(-2,~3,~-4\right)$. | 1 |
| 4598 | Find the angle between vectors $ \left(2,~6,~-3\right)$ and $\left(-2,~3,~-4\right)$. | 1 |
| 4599 | Find the angle between vectors $ \left(2,~3,~-4\right)$ and $\left(3,~-4,~5\right)$. | 1 |
| 4600 | Find the magnitude of the vector $ \| \vec{v} \| = \left(33,~22,~11\right) $ . | 1 |
