Vectors
(the database of solved problems)
All the problems and solutions shown below were generated using the Vectors Calculator.
| ID |
Problem |
Count |
| 2501 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-7,~8,~-2\right) $ and $ \vec{v_2} = \left(-1,~1,~0\right) $ . | 1 |
| 2502 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-4,~4\right) $ and $ \vec{v_2} = \left(-1,~-1\right) $ . | 1 |
| 2503 | Find the sum of the vectors $ \vec{v_1} = \left(2,~3,~1\right) $ and $ \vec{v_2} = \left(0,~5,~4\right) $ . | 1 |
| 2504 | Find the magnitude of the vector $ \| \vec{v} \| = \left(0,~0\right) $ . | 1 |
| 2505 | Calculate the cross product of the vectors $ \vec{v_1} = \left(5,~3,~0\right) $ and $ \vec{v_2} = \left(\dfrac{ 29 }{ 5 },~-\dfrac{ 9 }{ 10 },~0\right) $ . | 1 |
| 2506 | Find the angle between vectors $ \left(\dfrac{ 22 }{ 5 },~\dfrac{ 7 }{ 2 }\right)$ and $\left(-7,~\dfrac{ 53 }{ 10 }\right)$. | 1 |
| 2507 | Find the angle between vectors $ \left(-1,~-\dfrac{ 27 }{ 10 }\right)$ and $\left(-\dfrac{ 33 }{ 10 },~5\right)$. | 1 |
| 2508 | Find the magnitude of the vector $ \| \vec{v} \| = \left(4,~5\right) $ . | 1 |
| 2509 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-2,~-5\right) $ . | 1 |
| 2510 | Find the sum of the vectors $ \vec{v_1} = \left(9,~0\right) $ and $ \vec{v_2} = \left(1,~1\right) $ . | 1 |
| 2511 | Determine whether the vectors $ \vec{v_1} = \left(1,~-\sqrt{ 3 },~\dfrac{ 3 }{ 2 }\right) $, $ \vec{v_2} = \left(\sqrt{ 2 },~1,~\dfrac{ 2 }{ 3 }\right) $ and $ \vec{v_3} = \left(0,~0,~0\right)$ are linearly independent or dependent. | 1 |
| 2512 | Determine whether the vectors $ \vec{v_1} = \left(-1,~2,~3\right) $, $ \vec{v_2} = \left(4,~1,~-2\right) $ and $ \vec{v_3} = \left(-14,~-1,~16\right)$ are linearly independent or dependent. | 1 |
| 2513 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~-\sqrt{ 3 },~\dfrac{ 3 }{ 2 }\right) $ and $ \vec{v_2} = \left(\sqrt{ 2 },~1,~\dfrac{ 2 }{ 3 }\right) $ . | 1 |
| 2514 | Find the angle between vectors $ \left(2,~10\right)$ and $\left(4,~5\right)$. | 1 |
| 2515 | Find the sum of the vectors $ \vec{v_1} = \left(1,~3\right) $ and $ \vec{v_2} = \left(6,~10\right) $ . | 1 |
| 2516 | Calculate the dot product of the vectors $ \vec{v_1} = \left(4,~5\right) $ and $ \vec{v_2} = \left(66,~12\right) $ . | 1 |
| 2517 | Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~1,~4\right) $ and $ \vec{v_2} = \left(4,~-3,~8\right) $ . | 1 |
| 2518 | Find the angle between vectors $ \left(3,~4,~-5\right)$ and $\left(4,~-3,~5\right)$. | 1 |
| 2519 | Find the magnitude of the vector $ \| \vec{v} \| = \left(3,~2\right) $ . | 1 |
| 2520 | Find the magnitude of the vector $ \| \vec{v} \| = \left(1,~-2,~0\right) $ . | 1 |
| 2521 | Calculate the cross product of the vectors $ \vec{v_1} = \left(2,~7,~1\right) $ and $ \vec{v_2} = \left(-7,~-3,~0\right) $ . | 1 |
| 2522 | Calculate the cross product of the vectors $ \vec{v_1} = \left(2,~7,~-3\right) $ and $ \vec{v_2} = \left(-7,~-3,~0\right) $ . | 1 |
| 2523 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-5,~7,~-13\right) $ and $ \vec{v_2} = \left(4,~-12,~4\right) $ . | 1 |
| 2524 | Find the angle between vectors $ \left(-5,~7,~-13\right)$ and $\left(4,~-12,~4\right)$. | 1 |
| 2525 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~-2,~2\right) $ and $ \vec{v_2} = \left(0,~-1,~-2\right) $ . | 1 |
| 2526 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~-1,~0\right) $ and $ \vec{v_2} = \left(1,~-2,~2\right) $ . | 1 |
| 2527 | Find the magnitude of the vector $ \| \vec{v} \| = \left(1,~-2,~2\right) $ . | 1 |
| 2528 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~-2,~2\right) $ and $ \vec{v_2} = \left(0,~1,~-2\right) $ . | 1 |
| 2529 | Find the magnitude of the vector $ \| \vec{v} \| = \left(5,~7\right) $ . | 1 |
| 2530 | Calculate the cross product of the vectors $ \vec{v_1} = \left(\dfrac{ 2 }{ 3 },~\dfrac{ 1 }{ 3 },~-\dfrac{ 2 }{ 3 }\right) $ and $ \vec{v_2} = \left(\dfrac{ 1 }{ 3 },~-\dfrac{ 2 }{ 3 },~\dfrac{ 2 }{ 3 }\right) $ . | 1 |
| 2531 | Calculate the dot product of the vectors $ \vec{v_1} = \left(\dfrac{ 2 }{ 3 },~\dfrac{ 1 }{ 3 },~-\dfrac{ 2 }{ 3 }\right) $ and $ \vec{v_2} = \left(\dfrac{ 1 }{ 3 },~-\dfrac{ 2 }{ 3 },~\dfrac{ 2 }{ 3 }\right) $ . | 1 |
| 2532 | Find the difference of the vectors $ \vec{v_1} = \left(150,~0,~0\right) $ and $ \vec{v_2} = \left(-102,~\dfrac{ 122561 }{ 1000 },~0\right) $ . | 1 |
| 2533 | Find the difference of the vectors $ \vec{v_1} = \left(150,~0,~0\right) $ and $ \vec{v_2} = \left(-102,~122.561,~0\right) $ . | 1 |
| 2534 | Find the difference of the vectors $ \vec{v_1} = \left(1,~-4,~0\right) $ and $ \vec{v_2} = \left(-3,~8,~0\right) $ . | 1 |
| 2535 | Find the magnitude of the vector $ \| \vec{v} \| = \left(1,~-3,~2\right) $ . | 1 |
| 2536 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~-3,~2\right) $ and $ \vec{v_2} = \left(2,~1,~-1\right) $ . | 1 |
| 2537 | Find the magnitude of the vector $ \| \vec{v} \| = \left(2,~1\right) $ . | 1 |
| 2538 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-12,~2\right) $ and $ \vec{v_2} = \left(1,~6\right) $ . | 1 |
| 2539 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-3,~8\right) $ and $ \vec{v_2} = \left(-1,~-8\right) $ . | 1 |
| 2540 | Find the sum of the vectors $ \vec{v_1} = \left(5,~0\right) $ and $ \vec{v_2} = \left(4.3493,~4.8304\right) $ . | 1 |
| 2541 | Find the projection of the vector $ \vec{v_1} = \left(-7,~2\right) $ on the vector $ \vec{v_2} = \left(-1,~-3\right) $. | 1 |
| 2542 | Determine whether the vectors $ \vec{v_1} = \left(-8,~12,~4\right) $, $ \vec{v_2} = \left(6,~-9,~-3\right) $ and $ \vec{v_3} = \left(0,~0,~0\right)$ are linearly independent or dependent. | 1 |
| 2543 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-9,~9\right) $ . | 1 |
| 2544 | Find the difference of the vectors $ \vec{v_1} = \left(-1,~-4\right) $ and $ \vec{v_2} = \left(3,~2\right) $ . | 1 |
| 2545 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-4,~6\right) $ and $ \vec{v_2} = \left(-3,~-9\right) $ . | 1 |
| 2546 | Find the sum of the vectors $ \vec{v_1} = \left(0,~0\right) $ and $ \vec{v_2} = \left(3,~-2\right) $ . | 1 |
| 2547 | Calculate the cross product of the vectors $ \vec{v_1} = \left(7,~8,~9\right) $ and $ \vec{v_2} = \left(6,~-4,~5\right) $ . | 1 |
| 2548 | Find the angle between vectors $ \left(3,~3\right)$ and $\left(4,~4\right)$. | 1 |
| 2549 | Calculate the cross product of the vectors $ \vec{v_1} = \left(4,~5,~2\right) $ and $ \vec{v_2} = \left(6,~3,~1\right) $ . | 1 |
| 2550 | Calculate the cross product of the vectors $ \vec{v_1} = \left(6,~3,~1\right) $ and $ \vec{v_2} = \left(4,~5,~2\right) $ . | 1 |
