Vectors
(the database of solved problems)
All the problems and solutions shown below were generated using the Vectors Calculator.
| ID |
Problem |
Count |
| 5501 | Find the angle between vectors $ \left(5,~2\right)$ and $\left(-1,~-7\right)$. | 1 |
| 5502 | Find the angle between vectors $ \left(9,~-1\right)$ and $\left(-3,~1\right)$. | 1 |
| 5503 | Find the angle between vectors $ \left(-5,~1\right)$ and $\left(-4,~-1\right)$. | 1 |
| 5504 | Find the magnitude of the vector $ \| \vec{v} \| = \left(24,~-32\right) $ . | 1 |
| 5505 | Find the magnitude of the vector $ \| \vec{v} \| = \left(2,~-8\right) $ . | 1 |
| 5506 | Find the projection of the vector $ \vec{v_1} = \left(5,~0\right) $ on the vector $ \vec{v_2} = \left(3,~-1\right) $. | 1 |
| 5507 | Find the magnitude of the vector $ \| \vec{v} \| = \left(5,~0\right) $ . | 1 |
| 5508 | Calculate the dot product of the vectors $ \vec{v_1} = \left(5,~0\right) $ and $ \vec{v_2} = \left(3,~-1\right) $ . | 1 |
| 5509 | Find the angle between vectors $ \left(-2,~2\right)$ and $\left(8,~-1\right)$. | 1 |
| 5510 | Find the angle between vectors $ \left(1,~0\right)$ and $\left(2,~-8\right)$. | 1 |
| 5511 | Find the angle between vectors $ \left(0,~1\right)$ and $\left(2,~-8\right)$. | 1 |
| 5512 | Find the angle between vectors $ \left(3,~6\right)$ and $\left(3,~8\right)$. | 1 |
| 5513 | Find the angle between vectors $ \left(-8,~-2\right)$ and $\left(-3,~3\right)$. | 1 |
| 5514 | Find the angle between vectors $ \left(0,~-8\right)$ and $\left(-9,~-2\right)$. | 1 |
| 5515 | Find the angle between vectors $ \left(8,~2\right)$ and $\left(-7,~-3\right)$. | 1 |
| 5516 | Find the angle between vectors $ \left(-6,~0,~-3\right)$ and $\left(-6,~-\dfrac{ 9 }{ 2 },~0\right)$. | 1 |
| 5517 | Find the angle between vectors $ \left(-6,~2,~3\right)$ and $\left(-6,~-\dfrac{ 9 }{ 2 },~0\right)$. | 1 |
| 5518 | Find the projection of the vector $ \vec{v_1} = \left(-6,~-\dfrac{ 9 }{ 2 },~0\right) $ on the vector $ \vec{v_2} = \left(-6,~2,~3\right) $. | 1 |
| 5519 | Find the sum of the vectors $ \vec{v_1} = \left(4,~1\right) $ and $ \vec{v_2} = \left(3,~2\right) $ . | 1 |
| 5520 | Find the sum of the vectors $ \vec{v_1} = \left(4,~7,~-6\right) $ and $ \vec{v_2} = \left(4,~-9,~10\right) $ . | 1 |
| 5521 | Find the magnitude of the vector $ \| \vec{v} \| = \left(4,~7,~-6\right) $ . | 1 |
| 5522 | Calculate the dot product of the vectors $ \vec{v_1} = \left(4,~7,~-6\right) $ and $ \vec{v_2} = \left(4,~-9,~10\right) $ . | 1 |
| 5523 | Calculate the cross product of the vectors $ \vec{v_1} = \left(4,~7,~-6\right) $ and $ \vec{v_2} = \left(4,~-9,~10\right) $ . | 1 |
| 5524 | Find the sum of the vectors $ \vec{v_1} = \left(-3,~-1\right) $ and $ \vec{v_2} = \left(0,~0\right) $ . | 1 |
| 5525 | Find the difference of the vectors $ \vec{v_1} = \left(-18,~21\right) $ and $ \vec{v_2} = \left(8,~4\right) $ . | 1 |
| 5526 | Find the angle between vectors $ \left(7,~-11,~7\right)$ and $\left(6,~7,~10\right)$. | 1 |
| 5527 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~-4,~4\right) $ and $ \vec{v_2} = \left(0,~-4,~0\right) $ . | 1 |
| 5528 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~-4,~4\right) $ and $ \vec{v_2} = \left(-2,~-4,~3\right) $ . | 1 |
| 5529 | Calculate the dot product of the vectors $ \vec{v_1} = \left(0,~-4,~0\right) $ and $ \vec{v_2} = \left(0,~-4,~0\right) $ . | 1 |
| 5530 | Calculate the dot product of the vectors $ \vec{v_1} = \left(16,~-64,~64\right) $ and $ \vec{v_2} = \left(1,~-4,~4\right) $ . | 1 |
| 5531 | Determine whether the vectors $ \vec{v_1} = \left(1,~2,~-1\right) $, $ \vec{v_2} = \left(1,~1,~2\right) $ and $ \vec{v_3} = \left(0,~0,~0\right)$ are linearly independent or dependent. | 1 |
| 5532 | Find the angle between vectors $ \left(4,~0,~3\right)$ and $\left(-2,~3,~6\right)$. | 1 |
| 5533 | Find the angle between vectors $ \left(2,~3\right)$ and $\left(2,~1\right)$. | 1 |
| 5534 | Find the sum of the vectors $ \vec{v_1} = \left(0,~2,~5\right) $ and $ \vec{v_2} = \left(-2,~0,~0\right) $ . | 1 |
| 5535 | Find the difference of the vectors $ \vec{v_1} = \left(0,~2,~0\right) $ and $ \vec{v_2} = \left(5,~-2,~0\right) $ . | 1 |
| 5536 | Find the projection of the vector $ \vec{v_1} = \left(3,~1,~0\right) $ on the vector $ \vec{v_2} = \left(0,~1,~2\right) $. | 1 |
| 5537 | Find the difference of the vectors $ \vec{v_1} = \left(3,~-6\right) $ and $ \vec{v_2} = \left(0,~-9\right) $ . | 1 |
| 5538 | Find the sum of the vectors $ \vec{v_1} = \left(3,~8\right) $ and $ \vec{v_2} = \left(-4,~-2\right) $ . | 1 |
| 5539 | Find the projection of the vector $ \vec{v_1} = \left(2,~2\right) $ on the vector $ \vec{v_2} = \left(4,~-5\right) $. | 1 |
| 5540 | Find the magnitude of the vector $ \| \vec{v} \| = \left(2,~-1\right) $ . | 1 |
| 5541 | Find the difference of the vectors $ \vec{v_1} = \left(2,~-1\right) $ and $ \vec{v_2} = \left(2,~6\right) $ . | 1 |
| 5542 | Calculate the cross product of the vectors $ \vec{v_1} = \left(7,~-5,~1\right) $ and $ \vec{v_2} = \left(-3,~0,~-3\right) $ . | 1 |
| 5543 | Calculate the cross product of the vectors $ \vec{v_1} = \left(3,~-4,~-3\right) $ and $ \vec{v_2} = \left(0,~1,~6\right) $ . | 1 |
| 5544 | Find the magnitude of the vector $ \| \vec{v} \| = \left(12,~0,~0\right) $ . | 1 |
| 5545 | Calculate the cross product of the vectors $ \vec{v_1} = \left(7,~-1,~3\right) $ and $ \vec{v_2} = \left(-4,~-2,~5\right) $ . | 1 |
| 5546 | Find the sum of the vectors $ \vec{v_1} = \left(1,~-1\right) $ and $ \vec{v_2} = \left(3,~1\right) $ . | 1 |
| 5547 | Find the sum of the vectors $ \vec{v_1} = \left(1,~1\right) $ and $ \vec{v_2} = \left(2,~-1\right) $ . | 1 |
| 5548 | Find the sum of the vectors $ \vec{v_1} = \left(3,~-3\right) $ and $ \vec{v_2} = \left(-3,~1\right) $ . | 1 |
| 5549 | Find the sum of the vectors $ \vec{v_1} = \left(2,~4\right) $ and $ \vec{v_2} = \left(-1,~3\right) $ . | 1 |
| 5550 | Calculate the dot product of the vectors $ \vec{v_1} = \left(5,~12,~13\right) $ and $ \vec{v_2} = \left(3,~4,~5\right) $ . | 1 |
