Vectors – Solved Problems Database
All the problems and solutions shown below were generated using the Vectors Calculator.
ID |
Problem |
Count |
2501 | Find the sum of the vectors $ \vec{v_1} = \left(5,~1\right) $ and $ \vec{v_2} = \left(5,~-1\right) $ . | 1 |
2502 | Find the sum of the vectors $ \vec{v_1} = \left(-8,~6\right) $ and $ \vec{v_2} = \left(5,~-1\right) $ . | 1 |
2503 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~-3,~5\right) $ and $ \vec{v_2} = \left(3,~5,~-6\right) $ . | 1 |
2504 | Find the projection of the vector $ \vec{v_1} = \left(5,~0\right) $ on the vector $ \vec{v_2} = \left(1,~4\right) $. | 1 |
2505 | Find the difference of the vectors $ \vec{v_1} = \left(3,~-1\right) $ and $ \vec{v_2} = \left(12,~15\right) $ . | 1 |
2506 | Find the difference of the vectors $ \vec{v_1} = \left(4,~-2\right) $ and $ \vec{v_2} = \left(1,~4\right) $ . | 1 |
2507 | Find the magnitude of the vector $ \| \vec{v} \| = \left(\dfrac{ 2 }{ 3 },~\sqrt{ 3 },~2\right) $ . | 1 |
2508 | Find the difference of the vectors $ \vec{v_1} = \left(1,~-1\right) $ and $ \vec{v_2} = \left(-1,~-6\right) $ . | 1 |
2509 | Find the angle between vectors $ \left(-3,~4,~-4\right)$ and $\left(6,~4,~-1\right)$. | 1 |
2510 | Find the angle between vectors $ \left(2,~1,~3\right)$ and $\left(-3,~0,~1\right)$. | 1 |
2511 | Find the angle between vectors $ \left(-1,~-3\right)$ and $\left(-1,~4\right)$. | 1 |
2512 | Find the difference of the vectors $ \vec{v_1} = \left(3,~1,~1\right) $ and $ \vec{v_2} = \left(1,~5,~7\right) $ . | 1 |
2513 | Find the magnitude of the vector $ \| \vec{v} \| = \left(2,~1\right) $ . | 1 |
2514 | Find the angle between vectors $ \left(2,~6,~-3\right)$ and $\left(-2,~3,~-4\right)$. | 1 |
2515 | Find the difference of the vectors $ \vec{v_1} = \left(5,~1\right) $ and $ \vec{v_2} = \left(5,~-1\right) $ . | 1 |
2516 | Calculate the dot product of the vectors $ \vec{v_1} = \left(4,~6\right) $ and $ \vec{v_2} = \left(2,~3\right) $ . | 1 |
2517 | Calculate the dot product of the vectors $ \vec{v_1} = \left(4,~45\right) $ and $ \vec{v_2} = \left(7,~25\right) $ . | 1 |
2518 | Find the difference of the vectors $ \vec{v_1} = \left(-8,~-2\right) $ and $ \vec{v_2} = \left(5,~-5\right) $ . | 1 |
2519 | Find the magnitude of the vector $ \| \vec{v} \| = \left(\dfrac{ 2 }{ 3 },~\sqrt{ 3 },~2\right) $ . | 1 |
2520 | Find the difference of the vectors $ \vec{v_1} = \left(5,~2,~-1\right) $ and $ \vec{v_2} = \left(1,~-3,~2\right) $ . | 1 |
2521 | Calculate the dot product of the vectors $ \vec{v_1} = \left(8,~-13,~-4\right) $ and $ \vec{v_2} = \left(1,~-5,~9\right) $ . | 1 |
2522 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~-2,~2\right) $ and $ \vec{v_2} = \left(-2,~2,~1\right) $ . | 1 |
2523 | Find the angle between vectors $ \left(1,~-1\right)$ and $\left(-1,~-6\right)$. | 1 |
2524 | Calculate the dot product of the vectors $ \vec{v_1} = \left(12,~-9,~6\right) $ and $ \vec{v_2} = \left(-8,~6,~-4\right) $ . | 1 |
2525 | Find the angle between vectors $ \left(1,~1,~5\right)$ and $\left(5,~-5,~2\right)$. | 1 |
2526 | Find the difference of the vectors $ \vec{v_1} = \left(-3,~2\right) $ and $ \vec{v_2} = \left(4,~-5\right) $ . | 1 |
2527 | Find the magnitude of the vector $ \| \vec{v} \| = \left(2,~13\right) $ . | 1 |
2528 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-5,~5\right) $ . | 1 |
2529 | Find the projection of the vector $ \vec{v_1} = \left(0,~0,~0\right) $ on the vector $ \vec{v_2} = \left(0,~0,~0\right) $. | 1 |
2530 | Find the angle between vectors $ \left(4,~6\right)$ and $\left(2,~3\right)$. | 1 |
2531 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-1,~5\right) $ . | 1 |
2532 | Calculate the dot product of the vectors $ \vec{v_1} = \left(\dfrac{ 1 }{ 2 },~\sqrt{ 3 },~5\right) $ and $ \vec{v_2} = \left(4,~-\sqrt{ 3 },~10\right) $ . | 1 |
2533 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-3,~1,~-2\right) $ and $ \vec{v_2} = \left(1,~-1,~-1\right) $ . | 1 |
2534 | Find the sum of the vectors $ \vec{v_1} = \left(2,~3,~-3\right) $ and $ \vec{v_2} = \left(1,~4,~5\right) $ . | 1 |
2535 | Calculate the cross product of the vectors $ \vec{v_1} = \left(0,~3,~-6\right) $ and $ \vec{v_2} = \left(1,~2,~1\right) $ . | 1 |
2536 | Find the sum of the vectors $ \vec{v_1} = \left(4,~1\right) $ and $ \vec{v_2} = \left(3,~2\right) $ . | 1 |
2537 | Find the angle between vectors $ \left(4,~0,~3\right)$ and $\left(-2,~3,~6\right)$. | 1 |
2538 | Determine whether the vectors $ \vec{v_1} = \left(12,~-9,~6\right) $, $ \vec{v_2} = \left(-8,~6,~-4\right) $ and $ \vec{v_3} = \left(0,~0,~0\right)$ are linearly independent or dependent. | 1 |
2539 | Determine whether the vectors $ \vec{v_1} = \left(4,~9\right) $ and $ \vec{v_2} = \left(9,~4\right) $ are linearly independent or dependent. | 1 |
2540 | Find the magnitude of the vector $ \| \vec{v} \| = \left(17,~-11,~55\right) $ . | 1 |
2541 | Find the magnitude of the vector $ \| \vec{v} \| = \left(2,~9\right) $ . | 1 |
2542 | Determine whether the vectors $ \vec{v_1} = \left(2,~-1,~3\right) $, $ \vec{v_2} = \left(2,~1,~-2\right) $ and $ \vec{v_3} = \left(0,~0,~0\right)$ are linearly independent or dependent. | 1 |
2543 | Find the angle between vectors $ \left(2,~3,~-4\right)$ and $\left(3,~-4,~5\right)$. | 1 |
2544 | Find the magnitude of the vector $ \| \vec{v} \| = \left(6,~7\right) $ . | 1 |
2545 | Find the angle between vectors $ \left(6,~-4,~1\right)$ and $\left(3,~-2,~-3\right)$. | 1 |
2546 | Calculate the dot product of the vectors $ \vec{v_1} = \left(\sqrt{ 3 },~-1\right) $ and $ \vec{v_2} = \left(-1,~1\right) $ . | 1 |
2547 | Determine whether the vectors $ \vec{v_1} = \left(-3,~5\right) $ and $ \vec{v_2} = \left(-6,~10\right) $ are linearly independent or dependent. | 1 |
2548 | Calculate the dot product of the vectors $ \vec{v_1} = \left(\dfrac{ 1 }{ 2 },~\sqrt{ 3 },~5\right) $ and $ \vec{v_2} = \left(4,~-\sqrt{ 3 },~10\right) $ . | 1 |
2549 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-18,~-46\right) $ . | 1 |
2550 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~0,~2\right) $ and $ \vec{v_2} = \left(0,~3,~3\right) $ . | 1 |