Vectors – Solved Problems Database
All the problems and solutions shown below were generated using the Vectors Calculator.
ID |
Problem |
Count |
451 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-1,~-3\right) $ . | 2 |
452 | Find the difference of the vectors $ \vec{v_1} = \left(220,~20\right) $ and $ \vec{v_2} = \left(-150,~305.34\right) $ . | 2 |
453 | Find the magnitude of the vector $ \| \vec{v} \| = \left(3,~4\right) $ . | 2 |
454 | Find the angle between vectors $ \left(3,~2\right)$ and $\left(1,~-4\right)$. | 2 |
455 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~1,~2\right) $ and $ \vec{v_2} = \left(1,~1,~5\right) $ . | 2 |
456 | Find the angle between vectors $ \left(-4,~-3\right)$ and $\left(4,~3\right)$. | 2 |
457 | Calculate the dot product of the vectors $ \vec{v_1} = \left(8,~5\right) $ and $ \vec{v_2} = \left(-6,~-6\right) $ . | 2 |
458 | Find the difference of the vectors $ \vec{v_1} = \left(-2,~6\right) $ and $ \vec{v_2} = \left(6,~4\right) $ . | 2 |
459 | Find the angle between vectors $ \left(\sqrt{ 3 },~3\right)$ and $\left(1,~1\right)$. | 2 |
460 | Find the magnitude of the vector $ \| \vec{v} \| = \left(4,~3\right) $ . | 2 |
461 | Find the magnitude of the vector $ \| \vec{v} \| = \left(1,~-6\right) $ . | 2 |
462 | Find the sum of the vectors $ \vec{v_1} = \left(5,~4\right) $ and $ \vec{v_2} = \left(7,~-2\right) $ . | 2 |
463 | Find the difference of the vectors $ \vec{v_1} = \left(-5,~2\right) $ and $ \vec{v_2} = \left(-3,~7\right) $ . | 2 |
464 | Find the projection of the vector $ \vec{v_1} = \left(\sqrt{ 3 },~-1\right) $ on the vector $ \vec{v_2} = \left(0,~0\right) $. | 2 |
465 | Find the difference of the vectors $ \vec{v_1} = \left(6,~-3\right) $ and $ \vec{v_2} = \left(-2,~4\right) $ . | 2 |
466 | Find the difference of the vectors $ \vec{v_1} = \left(7,~9\right) $ and $ \vec{v_2} = \left(-30,~40\right) $ . | 2 |
467 | Find the magnitude of the vector $ \| \vec{v} \| = \left(\dfrac{ 2 }{ 3 },~\sqrt{ 3 },~2\right) $ . | 2 |
468 | Find the angle between vectors $ \left(7,~190\right)$ and $\left(3,~90\right)$. | 2 |
469 | Find the angle between vectors $ \left(-4,~-3\right)$ and $\left(3,~4\right)$. | 2 |
470 | Find the sum of the vectors $ \vec{v_1} = \left(-5,~1\right) $ and $ \vec{v_2} = \left(-8,~6\right) $ . | 2 |
471 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-5,~2\right) $ . | 2 |
472 | Find the sum of the vectors $ \vec{v_1} = \left(1,~0\right) $ and $ \vec{v_2} = \left(1.5,~0\right) $ . | 2 |
473 | Find the magnitude of the vector $ \| \vec{v} \| = \left(5,~8\right) $ . | 2 |
474 | Find the magnitude of the vector $ \| \vec{v} \| = \left(370,~-285.34\right) $ . | 2 |
475 | 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) $ . | 2 |
476 | Find the sum of the vectors $ \vec{v_1} = \left(7,~190\right) $ and $ \vec{v_2} = \left(3,~90\right) $ . | 2 |
477 | Find the difference of the vectors $ \vec{v_1} = \left(-5,~1\right) $ and $ \vec{v_2} = \left(-8,~6\right) $ . | 2 |
478 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-3,~-2\right) $ . | 2 |
479 | Determine whether the vectors $ \vec{v_1} = \left(1,~2,~5\right) $, $ \vec{v_2} = \left(2,~5,~1\right) $ and $ \vec{v_3} = \left(1,~5,~2\right)$ are linearly independent or dependent. | 2 |
480 | Find the magnitude of the vector $ \| \vec{v} \| = \left(\dfrac{ 19 }{ 100 },~\dfrac{ 81 }{ 100 }\right) $ . | 2 |
481 | Find the projection of the vector $ \vec{v_1} = \left(4,~-4\right) $ on the vector $ \vec{v_2} = \left(5,~-4\right) $. | 2 |
482 | Calculate the dot product of the vectors $ \vec{v_1} = \left(6,~-3\right) $ and $ \vec{v_2} = \left(-3,~-1\right) $ . | 2 |
483 | Find the difference of the vectors $ \vec{v_1} = \left(-5,~-10\right) $ and $ \vec{v_2} = \left(12,~7\right) $ . | 2 |
484 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-3,~5\right) $ . | 2 |
485 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-2,~3\right) $ . | 2 |
486 | Calculate the dot product of the vectors $ \vec{v_1} = \left(3020,~2800\right) $ and $ \vec{v_2} = \left(1,~1\right) $ . | 2 |
487 | Find the difference of the vectors $ \vec{v_1} = \left(-2,~3\right) $ and $ \vec{v_2} = \left(7,~-15\right) $ . | 2 |
488 | Calculate the dot product of the vectors $ \vec{v_1} = \left(4,~0,~3\right) $ and $ \vec{v_2} = \left(-2,~3,~6\right) $ . | 2 |
489 | Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~4\right) $ and $ \vec{v_2} = \left(5,~5\right) $ . | 2 |
490 | Find the difference of the vectors $ \vec{v_1} = \left(28,~-1\right) $ and $ \vec{v_2} = \left(-9,~0\right) $ . | 2 |
491 | Find the sum of the vectors $ \vec{v_1} = \left(3,~1\right) $ and $ \vec{v_2} = \left(-2,~-5\right) $ . | 2 |
492 | Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~2,~-4\right) $ and $ \vec{v_2} = \left(1,~0,~0\right) $ . | 2 |
493 | Find the angle between vectors $ \left(200,~0\right)$ and $\left(0,~20\right)$. | 2 |
494 | Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~-2\right) $ and $ \vec{v_2} = \left(-3,~2\right) $ . | 2 |
495 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-1,~-9\right) $ and $ \vec{v_2} = \left(4,~12\right) $ . | 2 |
496 | Find the magnitude of the vector $ \| \vec{v} \| = \left(3,~-3\right) $ . | 2 |
497 | Find the magnitude of the vector $ \| \vec{v} \| = \left(3,~-6\right) $ . | 2 |
498 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~1,~1\right) $ and $ \vec{v_2} = \left(2,~1,~0\right) $ . | 2 |
499 | Find the magnitude of the vector $ \| \vec{v} \| = \left(13,~2\right) $ . | 2 |
500 | Find the difference of the vectors $ \vec{v_1} = \left(-2,~3\right) $ and $ \vec{v_2} = \left(4,~-1\right) $ . | 2 |