Vectors
(the database of solved problems)
All the problems and solutions shown below were generated using the Vectors Calculator.
| ID |
Problem |
Count |
| 6451 | Find the magnitude of the vector $ \| \vec{v} \| = \left(1,~1,~4\right) $ . | 1 |
| 6452 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~1,~3\right) $ and $ \vec{v_2} = \left(0,~3,~3\right) $ . | 1 |
| 6453 | Find the difference of the vectors $ \vec{v_1} = \left(1,~2,~3\right) $ and $ \vec{v_2} = \left(2,~-1,~5\right) $ . | 1 |
| 6454 | Find the magnitude of the vector $ \| \vec{v} \| = \left(3,~-4\right) $ . | 1 |
| 6455 | Find the projection of the vector $ \vec{v_1} = \left(3,~-4\right) $ on the vector $ \vec{v_2} = \left(4,~3\right) $. | 1 |
| 6456 | Find the sum of the vectors $ \vec{v_1} = \left(-5,~3\right) $ and $ \vec{v_2} = \left(4,~-2\right) $ . | 1 |
| 6457 | Find the magnitude of the vector $ \| \vec{v} \| = \left(0,~1,~0\right) $ . | 1 |
| 6458 | Calculate the cross product of the vectors $ \vec{v_1} = \left(0,~0,~25\right) $ and $ \vec{v_2} = \left(\dfrac{ 329 }{ 500 },~\dfrac{ 6 }{ 25 },~0\right) $ . | 1 |
| 6459 | Calculate the cross product of the vectors $ \vec{v_1} = \left(0,~0,~25\right) $ and $ \vec{v_2} = \left(\dfrac{ 329 }{ 500 },~-\dfrac{ 239 }{ 1000 },~0\right) $ . | 1 |
| 6460 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-50,~0,~0\right) $ and $ \vec{v_2} = \left(\dfrac{ 329 }{ 500 },~-\dfrac{ 239 }{ 1000 },~0\right) $ . | 1 |
| 6461 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-50,~0,~0\right) $ and $ \vec{v_2} = \left(0,~0,~\dfrac{ 239 }{ 20 }\right) $ . | 1 |
| 6462 | Calculate the dot product of the vectors $ \vec{v_1} = \left(8,~-2,~1\right) $ and $ \vec{v_2} = \left(-2,~1,~0\right) $ . | 1 |
| 6463 | Find the magnitude of the vector $ \| \vec{v} \| = \left(8,~-2,~1\right) $ . | 1 |
| 6464 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-1,~-4,~1\right) $ . | 1 |
| 6465 | Calculate the cross product of the vectors $ \vec{v_1} = \left(8,~-2,~1\right) $ and $ \vec{v_2} = \left(-2,~1,~0\right) $ . | 1 |
| 6466 | Find the magnitude of the vector $ \| \vec{v} \| = \left(3,~2,~2\right) $ . | 1 |
| 6467 | Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~2,~2\right) $ and $ \vec{v_2} = \left(-1,~-4,~1\right) $ . | 1 |
| 6468 | Find the angle between vectors $ \left(3,~2,~2\right)$ and $\left(-1,~-4,~1\right)$. | 1 |
| 6469 | Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~2,~2\right) $ and $ \vec{v_2} = \left(-10,~5,~10\right) $ . | 1 |
| 6470 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-1,~-4,~1\right) $ and $ \vec{v_2} = \left(-10,~5,~10\right) $ . | 1 |
| 6471 | Find the magnitude of the vector $ \| \vec{v} \| = \left(3,~-1,~-2\right) $ . | 1 |
| 6472 | Find the magnitude of the vector $ \| \vec{v} \| = \left(1,~-1,~-2\right) $ . | 1 |
| 6473 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~-1,~-2\right) $ and $ \vec{v_2} = \left(3,~-1,~-2\right) $ . | 1 |
| 6474 | Calculate the dot product of the vectors $ \vec{v_1} = \left(0,~4,~-2\right) $ and $ \vec{v_2} = \left(3,~-1,~-2\right) $ . | 1 |
| 6475 | Calculate the dot product of the vectors $ \vec{v_1} = \left(0,~4,~-2\right) $ and $ \vec{v_2} = \left(1,~-1,~-2\right) $ . | 1 |
| 6476 | Find the angle between vectors $ \left(3,~-1,~-2\right)$ and $\left(1,~-1,~-2\right)$. | 1 |
| 6477 | Find the magnitude of the vector $ \| \vec{v} \| = \left(3,~-2,~0\right) $ . | 1 |
| 6478 | Find the magnitude of the vector $ \| \vec{v} \| = \left(3,~-2,~1\right) $ . | 1 |
| 6479 | Find the magnitude of the vector $ \| \vec{v} \| = \left(1,~2,~1\right) $ . | 1 |
| 6480 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~2,~1\right) $ and $ \vec{v_2} = \left(3,~2,~-1\right) $ . | 1 |
| 6481 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-4,~-2,~8\right) $ and $ \vec{v_2} = \left(3,~2,~-1\right) $ . | 1 |
| 6482 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-4,~-2,~8\right) $ and $ \vec{v_2} = \left(3,~-2,~1\right) $ . | 1 |
| 6483 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-4,~-2,~8\right) $ and $ \vec{v_2} = \left(1,~2,~1\right) $ . | 1 |
| 6484 | Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~-2,~1\right) $ and $ \vec{v_2} = \left(1,~2,~1\right) $ . | 1 |
| 6485 | Find the angle between vectors $ \left(3,~-2,~1\right)$ and $\left(1,~2,~1\right)$. | 1 |
| 6486 | Find the difference of the vectors $ \vec{v_1} = \left(-4,~7,~-2\right) $ and $ \vec{v_2} = \left(6,~1,~-4\right) $ . | 1 |
| 6487 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-3,~4,~0\right) $ and $ \vec{v_2} = \left(0,~3,~-3\right) $ . | 1 |
| 6488 | Calculate the cross product of the vectors $ \vec{v_1} = \left(0,~-1,~5\right) $ and $ \vec{v_2} = \left(5,~2,~0\right) $ . | 1 |
| 6489 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-2,~2\right) $ . | 1 |
| 6490 | Calculate the dot product of the vectors $ \vec{v_1} = \left(4,~45\right) $ and $ \vec{v_2} = \left(7,~25\right) $ . | 1 |
| 6491 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-3,~-3,~0\right) $ and $ \vec{v_2} = \left(0,~-2,~-3\right) $ . | 1 |
| 6492 | Calculate the cross product of the vectors $ \vec{v_1} = \left(4,~-2,~3\right) $ and $ \vec{v_2} = \left(3,~-1,~2\right) $ . | 1 |
| 6493 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~2,~3\right) $ and $ \vec{v_2} = \left(2,~5,~7\right) $ . | 1 |
| 6494 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-2,~1,~-3\right) $ and $ \vec{v_2} = \left(-1,~-3,~-5\right) $ . | 1 |
| 6495 | Determine whether the vectors $ \vec{v_1} = \left(1,~2,~12\right) $, $ \vec{v_2} = \left(4,~-7,~6\right) $ and $ \vec{v_3} = \left(7,~9,~9\right)$ are linearly independent or dependent. | 1 |
| 6496 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-2,~5,~3\right) $ and $ \vec{v_2} = \left(3,~-4,~-2\right) $ . | 1 |
| 6497 | Calculate the cross product of the vectors $ \vec{v_1} = \left(0,~4,~0\right) $ and $ \vec{v_2} = \left(-4,~-3,~0\right) $ . | 1 |
| 6498 | Find the angle between vectors $ \left(1,~2\right)$ and $\left(10,~5\right)$. | 1 |
| 6499 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-3,~-2\right) $ and $ \vec{v_2} = \left(4,~0\right) $ . | 1 |
| 6500 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~1,~0\right) $ and $ \vec{v_2} = \left(1,~0,~2\right) $ . | 1 |
