Vectors – Solved Problems Database
All the problems and solutions shown below were generated using the Vectors Calculator.
ID |
Problem |
Count |
501 | Find the magnitude of the vector $ \| \vec{v} \| = \left(0.8,~0.2\right) $ . | 2 |
502 | Find the difference of the vectors $ \vec{v_1} = \left(10,~0\right) $ and $ \vec{v_2} = \left(0,~2\right) $ . | 2 |
503 | Find the projection of the vector $ \vec{v_1} = \left(\sqrt{ 3 },~-1\right) $ on the vector $ \vec{v_2} = \left(-1,~1\right) $. | 2 |
504 | Find the difference of the vectors $ \vec{v_1} = \left(55,~-10\right) $ and $ \vec{v_2} = \left(30,~12\right) $ . | 2 |
505 | Find the difference of the vectors $ \vec{v_1} = \left(-20,~45\right) $ and $ \vec{v_2} = \left(37,~-1\right) $ . | 2 |
506 | Find the difference of the vectors $ \vec{v_1} = \left(210,~30\right) $ and $ \vec{v_2} = \left(-150,~309.23\right) $ . | 2 |
507 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-7,~-5\right) $ . | 2 |
508 | Find the magnitude of the vector $ \| \vec{v} \| = \left(200,~0\right) $ . | 2 |
509 | Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~-2\right) $ and $ \vec{v_2} = \left(-3,~4\right) $ . | 2 |
510 | Find the magnitude of the vector $ \| \vec{v} \| = \left(37,~40\right) $ . | 2 |
511 | Find the difference of the vectors $ \vec{v_1} = \left(-20,~45\right) $ and $ \vec{v_2} = \left(-37,~1\right) $ . | 2 |
512 | Find the magnitude of the vector $ \| \vec{v} \| = \left(45,~0\right) $ . | 2 |
513 | Find the sum of the vectors $ \vec{v_1} = \left(-2,~7\right) $ and $ \vec{v_2} = \left(4,~-5\right) $ . | 2 |
514 | Find the magnitude of the vector $ \| \vec{v} \| = \left(67,~85\right) $ . | 2 |
515 | Find the angle between vectors $ \left(-15,~-8\right)$ and $\left(-1,~3\right)$. | 2 |
516 | Find the magnitude of the vector $ \| \vec{v} \| = \left(5,~-1\right) $ . | 2 |
517 | Find the projection of the vector $ \vec{v_1} = \left(3020,~2800\right) $ on the vector $ \vec{v_2} = \left(1,~1\right) $. | 2 |
518 | Find the sum of the vectors $ \vec{v_1} = \left(-1,~4\right) $ and $ \vec{v_2} = \left(-4,~7\right) $ . | 2 |
519 | Determine whether the vectors $ \vec{v_1} = \left(1,~-6\right) $ and $ \vec{v_2} = \left(-15,~8\right) $ are linearly independent or dependent. | 2 |
520 | Find the sum of the vectors $ \vec{v_1} = \left(-20,~0\right) $ and $ \vec{v_2} = \left(16,~-3\right) $ . | 2 |
521 | Find the magnitude of the vector $ \| \vec{v} \| = \left(0,~-4\right) $ . | 2 |
522 | Find the difference of the vectors $ \vec{v_1} = \left(2,~4\right) $ and $ \vec{v_2} = \left(6,~2\right) $ . | 2 |
523 | Find the magnitude of the vector $ \| \vec{v} \| = \left(360,~-279.23\right) $ . | 2 |
524 | Find the sum of the vectors $ \vec{v_1} = \left(6,~-3\right) $ and $ \vec{v_2} = \left(-4,~6\right) $ . | 2 |
525 | Find the angle between vectors $ \left(\sqrt{ 3 },~-1\right)$ and $\left(-1,~1\right)$. | 2 |
526 | Find the angle between vectors $ \left(-4,~3\right)$ and $\left(2,~5\right)$. | 2 |
527 | Find the angle between vectors $ \left(1,~-12\right)$ and $\left(-\dfrac{ 1 }{ 4 },~3\right)$. | 2 |
528 | Find the magnitude of the vector $ \| \vec{v} \| = \left(9,~\sqrt{ 19 }\right) $ . | 2 |
529 | Calculate the cross product of the vectors $ \vec{v_1} = \left(4,~0,~3\right) $ and $ \vec{v_2} = \left(-2,~3,~6\right) $ . | 2 |
530 | Find the sum of the vectors $ \vec{v_1} = \left(-2,~9\right) $ and $ \vec{v_2} = \left(5,~6\right) $ . | 2 |
531 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-4,~-2\right) $ and $ \vec{v_2} = \left(-4,~-4\right) $ . | 2 |
532 | Calculate the dot product of the vectors $ \vec{v_1} = \left(200,~0\right) $ and $ \vec{v_2} = \left(0,~20\right) $ . | 2 |
533 | Find the angle between vectors $ \left(-\sqrt{ 3 },~-1\right)$ and $\left(-1,~1\right)$. | 2 |
534 | Determine whether the vectors $ \vec{v_1} = \left(1,~-12\right) $ and $ \vec{v_2} = \left(-\dfrac{ 1 }{ 4 },~3\right) $ are linearly independent or dependent. | 2 |
535 | Find the sum of the vectors $ \vec{v_1} = \left(5,~2\right) $ and $ \vec{v_2} = \left(9,~-4\right) $ . | 2 |
536 | Find the magnitude of the vector $ \| \vec{v} \| = \left(4,~1\right) $ . | 2 |
537 | Find the magnitude of the vector $ \| \vec{v} \| = \left(\dfrac{ 39 }{ 10 },~0\right) $ . | 2 |
538 | Find the magnitude of the vector $ \| \vec{v} \| = \left(6,~8\right) $ . | 2 |
539 | Find the difference of the vectors $ \vec{v_1} = \left(-4,~-3\right) $ and $ \vec{v_2} = \left(-9,~27\right) $ . | 2 |
540 | Find the magnitude of the vector $ \| \vec{v} \| = \left(1,~13\right) $ . | 2 |
541 | Find the difference of the vectors $ \vec{v_1} = \left(240,~40\right) $ and $ \vec{v_2} = \left(-190,~321.43\right) $ . | 2 |
542 | Find the angle between vectors $ \left(9,~-8\right)$ and $\left(2,~-12\right)$. | 2 |
543 | Find the sum of the vectors $ \vec{v_1} = \left(3,~5\right) $ and $ \vec{v_2} = \left(6,~0\right) $ . | 2 |
544 | Find the sum of the vectors $ \vec{v_1} = \left(120000,~30\right) $ and $ \vec{v_2} = \left(40000,~-90\right) $ . | 2 |
545 | Find the magnitude of the vector $ \| \vec{v} \| = \left(\dfrac{ 39 }{ 10 },~\dfrac{ 23 }{ 20 }\right) $ . | 2 |
546 | Find the magnitude of the vector $ \| \vec{v} \| = \left(8,~7\right) $ . | 2 |
547 | Find the magnitude of the vector $ \| \vec{v} \| = \left(17,~8\right) $ . | 2 |
548 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-3,~-9\right) $ . | 2 |
549 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-\dfrac{ 4 }{ 3 },~\dfrac{ 5 }{ 2 }\right) $ and $ \vec{v_2} = \left(16,~-30\right) $ . | 2 |
550 | Find the angle between vectors $ \left(\sqrt{ 3 },~-3\right)$ and $\left(1,~-1\right)$. | 2 |