Vectors – Solved Problems Database
All the problems and solutions shown below were generated using the Vectors Calculator.
ID |
Problem |
Count |
2451 | Calculate the cross product of the vectors $ \vec{v_1} = \left(2,~1,~-2\right) $ and $ \vec{v_2} = \left(2,~3,~3\right) $ . | 1 |
2452 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-4,~4\right) $ and $ \vec{v_2} = \left(-1,~-1\right) $ . | 1 |
2453 | Calculate the cross product of the vectors $ \vec{v_1} = \left(0,~1,~1\right) $ and $ \vec{v_2} = \left(2,~0,~3\right) $ . | 1 |
2454 | Find the magnitude of the vector $ \| \vec{v} \| = \left(0,~4,~0\right) $ . | 1 |
2455 | Find the angle between vectors $ \left(-5,~5\right)$ and $\left(4,~-7\right)$. | 1 |
2456 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~-2,~3\right) $ and $ \vec{v_2} = \left(-12,~-12,~-4\right) $ . | 1 |
2457 | Calculate the dot product of the vectors $ \vec{v_1} = \left(\dfrac{ 1 }{ 3 },~\dfrac{ 2 }{ 3 },~\dfrac{ 2 }{ 3 }\right) $ and $ \vec{v_2} = \left(-\dfrac{ 2 }{ 3 },~\dfrac{ 2 }{ 3 },~-\dfrac{ 1 }{ 3 }\right) $ . | 1 |
2458 | 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 |
2459 | Calculate the cross product of the vectors $ \vec{v_1} = \left(3,~2,~0\right) $ and $ \vec{v_2} = \left(1,~-2,~-1\right) $ . | 1 |
2460 | Find the angle between vectors $ \left(2,~-3,~4\right)$ and $\left(-1,~\dfrac{ 3 }{ 2 },~-2\right)$. | 1 |
2461 | Calculate the dot product of the vectors $ \vec{v_1} = \left(5,~5\right) $ and $ \vec{v_2} = \left(5,~-2\right) $ . | 1 |
2462 | Calculate the dot product of the vectors $ \vec{v_1} = \left(4,~-1,~5\right) $ and $ \vec{v_2} = \left(-1,~-1,~0\right) $ . | 1 |
2463 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-1,~34,~19\right) $ and $ \vec{v_2} = \left(1,~0,~2\right) $ . | 1 |
2464 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-2,~2,~1\right) $ . | 1 |
2465 | Find the sum of the vectors $ \vec{v_1} = \left(2,~-5\right) $ and $ \vec{v_2} = \left(-3,~-5\right) $ . | 1 |
2466 | Find the angle between vectors $ \left(-4,~4\right)$ and $\left(-4,~4\right)$. | 1 |
2467 | Find the sum of the vectors $ \vec{v_1} = \left(-3,~-11\right) $ and $ \vec{v_2} = \left(4,~5\right) $ . | 1 |
2468 | Find the sum of the vectors $ \vec{v_1} = \left(4,~-5\right) $ and $ \vec{v_2} = \left(-2,~7\right) $ . | 1 |
2469 | Find the angle between vectors $ \left(4,~-4\right)$ and $\left(5,~-4\right)$. | 1 |
2470 | 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(1,~2,~1\right)$ are linearly independent or dependent. | 1 |
2471 | Find the magnitude of the vector $ \| \vec{v} \| = \left(0,~9\right) $ . | 1 |
2472 | Find the angle between vectors $ \left(-2,~1,~1\right)$ and $\left(1,~-3,~-1\right)$. | 1 |
2473 | Find the sum of the vectors $ \vec{v_1} = \left(5,~0\right) $ and $ \vec{v_2} = \left(1,~4\right) $ . | 1 |
2474 | Find the angle between vectors $ \left(5,~-4,~-3\right)$ and $\left(2,~1,~2\right)$. | 1 |
2475 | Calculate the dot product of the vectors $ \vec{v_1} = \left(4,~-5,~-4\right) $ and $ \vec{v_2} = \left(0,~-4,~-5\right) $ . | 1 |
2476 | Find the sum of the vectors $ \vec{v_1} = \left(1,~-6\right) $ and $ \vec{v_2} = \left(-15,~8\right) $ . | 1 |
2477 | Calculate the dot product of the vectors $ \vec{v_1} = \left(5,~3,~0\right) $ and $ \vec{v_2} = \left(1,~0,~5\right) $ . | 1 |
2478 | Find the angle between vectors $ \left(2,~10\right)$ and $\left(4,~5\right)$. | 1 |
2479 | Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~1,~-1\right) $ and $ \vec{v_2} = \left(1,~-1,~-1\right) $ . | 1 |
2480 | Find the projection of the vector $ \vec{v_1} = \left(\sqrt{ 3 },~3\right) $ on the vector $ \vec{v_2} = \left(1,~1\right) $. | 1 |
2481 | Find the sum of the vectors $ \vec{v_1} = \left(\dfrac{ 49 }{ 100 },~0\right) $ and $ \vec{v_2} = \left(\dfrac{ 27 }{ 500 },~\dfrac{ 12 }{ 25 }\right) $ . | 1 |
2482 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-2,~2\right) $ . | 1 |
2483 | Find the sum of the vectors $ \vec{v_1} = \left(3,~-1\right) $ and $ \vec{v_2} = \left(12,~15\right) $ . | 1 |
2484 | Find the magnitude of the vector $ \| \vec{v} \| = \left(24,~27\right) $ . | 1 |
2485 | Find the difference of the vectors $ \vec{v_1} = \left(3,~2,~-3\right) $ and $ \vec{v_2} = \left(2,~-2,~1\right) $ . | 1 |
2486 | Find the sum of the vectors $ \vec{v_1} = \left(-8,~-2\right) $ and $ \vec{v_2} = \left(5,~-5\right) $ . | 1 |
2487 | Find the sum of the vectors $ \vec{v_1} = \left(5,~2,~-1\right) $ and $ \vec{v_2} = \left(1,~-3,~2\right) $ . | 1 |
2488 | Calculate the cross product of the vectors $ \vec{v_1} = \left(3,~4,~-7\right) $ and $ \vec{v_2} = \left(1,~0,~2\right) $ . | 1 |
2489 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~-2,~2\right) $ and $ \vec{v_2} = \left(-2,~2,~1\right) $ . | 1 |
2490 | Find the magnitude of the vector $ \| \vec{v} \| = \left(3,~4\right) $ . | 1 |
2491 | Find the projection of the vector $ \vec{v_1} = \left(3,~-6,~-1\right) $ on the vector $ \vec{v_2} = \left(1,~4,~-5\right) $. | 1 |
2492 | Find the angle between vectors $ \left(-4,~-4\right)$ and $\left(-4,~4\right)$. | 1 |
2493 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-3,~4,~-4\right) $ and $ \vec{v_2} = \left(6,~4,~-1\right) $ . | 1 |
2494 | Calculate the dot product of the vectors $ \vec{v_1} = \left(4,~-5,~-4\right) $ and $ \vec{v_2} = \left(-3,~1,~2\right) $ . | 1 |
2495 | Determine whether the vectors $ \vec{v_1} = \left(2,~1,~3\right) $, $ \vec{v_2} = \left(-3,~0,~1\right) $ and $ \vec{v_3} = \left(0,~0,~0\right)$ are linearly independent or dependent. | 1 |
2496 | Find the sum of the vectors $ \vec{v_1} = \left(6,~9,~-1\right) $ and $ \vec{v_2} = \left(6,~-7,~0\right) $ . | 1 |
2497 | Determine whether the vectors $ \vec{v_1} = \left(-3,~6\right) $ and $ \vec{v_2} = \left(10,~5\right) $ are linearly independent or dependent. | 1 |
2498 | Find the magnitude of the vector $ \| \vec{v} \| = \left(6,~15,~1\right) $ . | 1 |
2499 | Find the sum of the vectors $ \vec{v_1} = \left(2,~-5\right) $ and $ \vec{v_2} = \left(1,~-7\right) $ . | 1 |
2500 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~-1,~2\right) $ and $ \vec{v_2} = \left(3,~2,~-2\right) $ . | 1 |