Vectors
(the database of solved problems)
All the problems and solutions shown below were generated using the Vectors Calculator.
| ID |
Problem |
Count |
| 4501 | Find the angle between vectors $ \left(-\dfrac{ 81 }{ 1000 },~-\dfrac{ 327 }{ 500 }\right)$ and $\left(-\dfrac{ 47 }{ 125 },~\dfrac{ 151 }{ 1000 }\right)$. | 1 |
| 4502 | Find the magnitude of the vector $ \| \vec{v} \| = \left(3,~0\right) $ . | 1 |
| 4503 | Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~2\right) $ and $ \vec{v_2} = \left(2,~-3\right) $ . | 1 |
| 4504 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-4,~6\right) $ and $ \vec{v_2} = \left(2,~-3\right) $ . | 1 |
| 4505 | Calculate the cross product of the vectors $ \vec{v_1} = \left(2,~3,~0\right) $ and $ \vec{v_2} = \left(2,~3,~0\right) $ . | 1 |
| 4506 | Find the angle between vectors $ \left(-15,~4,~-3\right)$ and $\left(8,~-1,~4\right)$. | 1 |
| 4507 | Find the angle between vectors $ \left(-6,~6\right)$ and $\left(-7,~-6\right)$. | 1 |
| 4508 | Find the angle between vectors $ \left(-8,~7,~8\right)$ and $\left(4,~-6,~1\right)$. | 1 |
| 4509 | Find the angle between vectors $ \left(2,~-3,~-4\right)$ and $\left(-3,~1,~-1\right)$. | 1 |
| 4510 | Find the angle between vectors $ \left(3,~4\right)$ and $\left(12,~5\right)$. | 1 |
| 4511 | Find the magnitude of the vector $ \| \vec{v} \| = \left(6,~0\right) $ . | 1 |
| 4512 | Find the magnitude of the vector $ \| \vec{v} \| = \left(7,~1\right) $ . | 1 |
| 4513 | Calculate the cross product of the vectors $ \vec{v_1} = \left(0,~2,~1\right) $ and $ \vec{v_2} = \left(1,~0,~2\right) $ . | 1 |
| 4514 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-4,~6,~-5\right) $ and $ \vec{v_2} = \left(-4,~1,~-1\right) $ . | 1 |
| 4515 | Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~1\right) $ and $ \vec{v_2} = \left(1,~2\right) $ . | 1 |
| 4516 | 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 |
| 4517 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~0,~1\right) $ and $ \vec{v_2} = \left(-1,~-1,~-1\right) $ . | 1 |
| 4518 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~0,~2\right) $ and $ \vec{v_2} = \left(0,~2,~1\right) $ . | 1 |
| 4519 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-7,~9,~6\right) $ and $ \vec{v_2} = \left(8,~3,~-2\right) $ . | 1 |
| 4520 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-7,~9,~6\right) $ and $ \vec{v_2} = \left(-8,~3,~-2\right) $ . | 1 |
| 4521 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-2,~-4,~-2\right) $ and $ \vec{v_2} = \left(8,~-4,~1\right) $ . | 1 |
| 4522 | Find the sum of the vectors $ \vec{v_1} = \left(8,~7\right) $ and $ \vec{v_2} = \left(-6,~4\right) $ . | 1 |
| 4523 | Find the magnitude of the vector $ \| \vec{v} \| = \left(1,~-2\right) $ . | 1 |
| 4524 | Find the angle between vectors $ \left(1,~-2\right)$ and $\left(5,~3\right)$. | 1 |
| 4525 | Find the sum of the vectors $ \vec{v_1} = \left(1,~-2\right) $ and $ \vec{v_2} = \left(5,~3\right) $ . | 1 |
| 4526 | Find the magnitude of the vector $ \| \vec{v} \| = \left(6,~1\right) $ . | 1 |
| 4527 | Calculate the dot product of the vectors $ \vec{v_1} = \left(9,~-3\right) $ and $ \vec{v_2} = \left(1,~-1\right) $ . | 1 |
| 4528 | Find the angle between vectors $ \left(1275,~2500\right)$ and $\left(\dfrac{ 66 }{ 5 },~\dfrac{ 41 }{ 5 }\right)$. | 1 |
| 4529 | Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~1\right) $ and $ \vec{v_2} = \left(-5,~3\right) $ . | 1 |
| 4530 | Find the sum of the vectors $ \vec{v_1} = \left(3,~4\right) $ and $ \vec{v_2} = \left(2,~8\right) $ . | 1 |
| 4531 | Determine whether the vectors $ \vec{v_1} = \left(3,~4\right) $ and $ \vec{v_2} = \left(2,~8\right) $ are linearly independent or dependent. | 1 |
| 4532 | Find the angle between vectors $ \left(-2,~1\right)$ and $\left(1,~-4\right)$. | 1 |
| 4533 | Find the projection of the vector $ \vec{v_1} = \left(-7,~24\right) $ on the vector $ \vec{v_2} = \left(0,~0\right) $. | 1 |
| 4534 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-7,~24\right) $ and $ \vec{v_2} = \left(0,~0\right) $ . | 1 |
| 4535 | Calculate the dot product of the vectors $ \vec{v_1} = \left(5,~-4\right) $ and $ \vec{v_2} = \left(-2,~4\right) $ . | 1 |
| 4536 | Find the angle between vectors $ \left(2,~-5\right)$ and $\left(-4,~10\right)$. | 1 |
| 4537 | Find the angle between vectors $ \left(4,~5\right)$ and $\left(-5,~11\right)$. | 1 |
| 4538 | Calculate the dot product of the vectors $ \vec{v_1} = \left(4,~5\right) $ and $ \vec{v_2} = \left(-5,~11\right) $ . | 1 |
| 4539 | Find the projection of the vector $ \vec{v_1} = \left(4,~5\right) $ on the vector $ \vec{v_2} = \left(-5,~11\right) $. | 1 |
| 4540 | Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~3\right) $ and $ \vec{v_2} = \left(1,~1\right) $ . | 1 |
| 4541 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-3,~-1\right) $ . | 1 |
| 4542 | Find the sum of the vectors $ \vec{v_1} = \left(-3,~-1\right) $ and $ \vec{v_2} = \left(1,~4\right) $ . | 1 |
| 4543 | Find the sum of the vectors $ \vec{v_1} = \left(-3,~1\right) $ and $ \vec{v_2} = \left(-1,~4\right) $ . | 1 |
| 4544 | Determine whether the vectors $ \vec{v_1} = \left(1,~-3\right) $ and $ \vec{v_2} = \left(-2,~6\right) $ are linearly independent or dependent. | 1 |
| 4545 | Find the difference of the vectors $ \vec{v_1} = \left(3,~1,~1\right) $ and $ \vec{v_2} = \left(1,~5,~7\right) $ . | 1 |
| 4546 | Calculate the dot product of the vectors $ \vec{v_1} = \left(4,~1,~-1\right) $ and $ \vec{v_2} = \left(-2,~1,~-5\right) $ . | 1 |
| 4547 | Calculate the dot product of the vectors $ \vec{v_1} = \left(5,~3,~4\right) $ and $ \vec{v_2} = \left(6,~-8,~-1\right) $ . | 1 |
| 4548 | Find the angle between vectors $ \left(5,~3,~4\right)$ and $\left(6,~-8,~-1\right)$. | 1 |
| 4549 | Find the magnitude of the vector $ \| \vec{v} \| = \left(0.2,~0.2,~0.2\right) $ . | 1 |
| 4550 | Determine whether the vectors $ \vec{v_1} = \left(0.2,~0.2,~0.2\right) $, $ \vec{v_2} = \left(0.2,~0.4,~0.3\right) $ and $ \vec{v_3} = \left(0.6,~0.4,~0.5\right)$ are linearly independent or dependent. | 1 |
