Vectors
(the database of solved problems)
All the problems and solutions shown below were generated using the Vectors Calculator.
| ID |
Problem |
Count |
| 5451 | Calculate the cross product of the vectors $ \vec{v_1} = \left(6,~7,~-2\right) $ and $ \vec{v_2} = \left(3,~-1,~7\right) $ . | 1 |
| 5452 | Find the projection of the vector $ \vec{v_1} = \left(3,~-2\right) $ on the vector $ \vec{v_2} = \left(3,~-2\right) $. | 1 |
| 5453 | Find the magnitude of the vector $ \| \vec{v} \| = \left(9,~14\right) $ . | 1 |
| 5454 | Find the angle between vectors $ \left(-5,~2\right)$ and $\left(-\dfrac{ 72 }{ 17 },~-\dfrac{ 18 }{ 17 }\right)$. | 1 |
| 5455 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-3,~1,~2\right) $ and $ \vec{v_2} = \left(1,~0,~2\right) $ . | 1 |
| 5456 | Find the magnitude of the vector $ \| \vec{v} \| = \left(6,~-2,~-6\right) $ . | 1 |
| 5457 | Find the magnitude of the vector $ \| \vec{v} \| = \left(3,~-2\right) $ . | 1 |
| 5458 | Find the sum of the vectors $ \vec{v_1} = \left(3,~-2\right) $ and $ \vec{v_2} = \left(-1,~-4\right) $ . | 1 |
| 5459 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~1,~1\right) $ and $ \vec{v_2} = \left(3,~0,~0\right) $ . | 1 |
| 5460 | Find the magnitude of the vector $ \| \vec{v} \| = \left(\dfrac{ 2 }{ 5 },~\dfrac{ 3 }{ 10 }\right) $ . | 1 |
| 5461 | Find the magnitude of the vector $ \| \vec{v} \| = \left(1500,~1500\right) $ . | 1 |
| 5462 | Find the angle between vectors $ \left(2,~2,~2\right)$ and $\left(2,~-2,~2\right)$. | 1 |
| 5463 | Find the sum of the vectors $ \vec{v_1} = \left(0,~-1,~-2\right) $ and $ \vec{v_2} = \left(-3,~1,~0\right) $ . | 1 |
| 5464 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~-5,~0\right) $ and $ \vec{v_2} = \left(-5,~1,~0\right) $ . | 1 |
| 5465 | Find the sum of the vectors $ \vec{v_1} = \left(2,~7\right) $ and $ \vec{v_2} = \left(3,~1\right) $ . | 1 |
| 5466 | Find the angle between vectors $ \left(-1,~-2\right)$ and $\left(-2,~3\right)$. | 1 |
| 5467 | Find the difference of the vectors $ \vec{v_1} = \left(5,~8\right) $ and $ \vec{v_2} = \left(7,~3\right) $ . | 1 |
| 5468 | Find the magnitude of the vector $ \| \vec{v} \| = \left(3,~0\right) $ . | 1 |
| 5469 | Find the sum of the vectors $ \vec{v_1} = \left(0,~0,~-5\right) $ and $ \vec{v_2} = \left(-4,~0,~-5\right) $ . | 1 |
| 5470 | Find the sum of the vectors $ \vec{v_1} = \left(-2,~-\dfrac{ 3 }{ 2 }\right) $ and $ \vec{v_2} = \left(-\dfrac{ 3 }{ 2 },~\dfrac{ 5 }{ 2 }\right) $ . | 1 |
| 5471 | Find the angle between vectors $ \left(-4,~5\right)$ and $\left(-1,~2\right)$. | 1 |
| 5472 | Find the magnitude of the vector $ \| \vec{v} \| = \left(2,~-2\right) $ . | 1 |
| 5473 | Find the sum of the vectors $ \vec{v_1} = \left(-4,~-5\right) $ and $ \vec{v_2} = \left(2,~-2\right) $ . | 1 |
| 5474 | Find the difference of the vectors $ \vec{v_1} = \left(2,~-2\right) $ and $ \vec{v_2} = \left(3,~5\right) $ . | 1 |
| 5475 | Find the magnitude of the vector $ \| \vec{v} \| = \left(2,~4,~6\right) $ . | 1 |
| 5476 | Find the projection of the vector $ \vec{v_1} = \left(2,~4,~6\right) $ on the vector $ \vec{v_2} = \left(1,~3,~5\right) $. | 1 |
| 5477 | Find the magnitude of the vector $ \| \vec{v} \| = \left(1,~2,~-3\right) $ . | 1 |
| 5478 | Find the difference of the vectors $ \vec{v_1} = \left(-28,~-35\right) $ and $ \vec{v_2} = \left(8,~-8\right) $ . | 1 |
| 5479 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-4,~-6\right) $ . | 1 |
| 5480 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~2,~3\right) $ and $ \vec{v_2} = \left(-3,~-1,~2\right) $ . | 1 |
| 5481 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-4,~-2,~-4\right) $ and $ \vec{v_2} = \left(5,~5,~2\right) $ . | 1 |
| 5482 | Find the angle between vectors $ \left(4,~-3\right)$ and $\left(8,~6\right)$. | 1 |
| 5483 | Find the angle between vectors $ \left(4,~-3\right)$ and $\left(8,~-9\right)$. | 1 |
| 5484 | Find the angle between vectors $ \left(4,~-3\right)$ and $\left(-3,~4\right)$. | 1 |
| 5485 | Find the angle between vectors $ \left(4,~-3\right)$ and $\left(20,~-15\right)$. | 1 |
| 5486 | Determine whether the vectors $ \vec{v_1} = \left(2,~5\right) $ and $ \vec{v_2} = \left(25,~-10\right) $ are linearly independent or dependent. | 1 |
| 5487 | Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~5\right) $ and $ \vec{v_2} = \left(25,~-10\right) $ . | 1 |
| 5488 | Find the sum of the vectors $ \vec{v_1} = \left(8,~0,~2\right) $ and $ \vec{v_2} = \left(1,~-4,~4\right) $ . | 1 |
| 5489 | Calculate the cross product of the vectors $ \vec{v_1} = \left(3,~1,~-2\right) $ and $ \vec{v_2} = \left(1,~3,~4\right) $ . | 1 |
| 5490 | Find the sum of the vectors $ \vec{v_1} = \left(2,~6,~2\right) $ and $ \vec{v_2} = \left(1,~-4,~4\right) $ . | 1 |
| 5491 | Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~3,~0\right) $ and $ \vec{v_2} = \left(2,~0,~-1\right) $ . | 1 |
| 5492 | Find the angle between vectors $ \left(2,~-9\right)$ and $\left(-5,~5\right)$. | 1 |
| 5493 | Find the sum of the vectors $ \vec{v_1} = \left(-1,~-6\right) $ and $ \vec{v_2} = \left(-6,~8\right) $ . | 1 |
| 5494 | Determine whether the vectors $ \vec{v_1} = \left(2,~5\right) $ and $ \vec{v_2} = \left(-2,~1\right) $ are linearly independent or dependent. | 1 |
| 5495 | Find the magnitude of the vector $ \| \vec{v} \| = \left(2,~5\right) $ . | 1 |
| 5496 | Find the angle between vectors $ \left(2,~5\right)$ and $\left(-2,~1\right)$. | 1 |
| 5497 | Find the difference of the vectors $ \vec{v_1} = \left(\dfrac{ 3489 }{ 10000 },~\dfrac{ 6199 }{ 10000 },~\dfrac{ 1927 }{ 5000 }\right) $ and $ \vec{v_2} = \left(\dfrac{ 359 }{ 1000 },~\dfrac{ 65487 }{ 100000 },~\dfrac{ 22241 }{ 50000 }\right) $ . | 1 |
| 5498 | Find the angle between vectors $ \left(-7,~-2\right)$ and $\left(-6,~-5\right)$. | 1 |
| 5499 | Find the magnitude of the vector $ \| \vec{v} \| = \left(\dfrac{ 101 }{ 10000 },~\dfrac{ 3497 }{ 100000 },~\dfrac{ 2971 }{ 50000 }\right) $ . | 1 |
| 5500 | Find the angle between vectors $ \left(-7,~6\right)$ and $\left(-7,~-4\right)$. | 1 |
