Vectors
(the database of solved problems)
All the problems and solutions shown below were generated using the Vectors Calculator.
| ID |
Problem |
Count |
| 3451 | Find the difference of the vectors $ \vec{v_1} = \left(4,~7\right) $ and $ \vec{v_2} = \left(5,~-2\right) $ . | 1 |
| 3452 | Find the magnitude of the vector $ \| \vec{v} \| = \left(3,~3\right) $ . | 1 |
| 3453 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-3,~8,~0\right) $ and $ \vec{v_2} = \left(23,~6,~0\right) $ . | 1 |
| 3454 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-3,~8,~0\right) $ and $ \vec{v_2} = \left(-6,~6,~0\right) $ . | 1 |
| 3455 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-3,~8,~0\right) $ and $ \vec{v_2} = \left(-1,~6,~0\right) $ . | 1 |
| 3456 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-3,~8,~0\right) $ and $ \vec{v_2} = \left(-\dfrac{ 3 }{ 2 },~6,~0\right) $ . | 1 |
| 3457 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-3,~8,~0\right) $ and $ \vec{v_2} = \left(0,~6,~0\right) $ . | 1 |
| 3458 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-3,~8,~0\right) $ and $ \vec{v_2} = \left(0,~6,~0\right) $ . | 1 |
| 3459 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-3,~8,~0\right) $ and $ \vec{v_2} = \left(-8,~6,~0\right) $ . | 1 |
| 3460 | Calculate the cross product of the vectors $ \vec{v_1} = \left(5,~1,~-2\right) $ and $ \vec{v_2} = \left(10,~3,~-6\right) $ . | 1 |
| 3461 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-6,~2,~8\right) $ and $ \vec{v_2} = \left(9,~3,~1\right) $ . | 1 |
| 3462 | Find the difference of the vectors $ \vec{v_1} = \left(1,~1,~1\right) $ and $ \vec{v_2} = \left(2,~2,~0\right) $ . | 1 |
| 3463 | Find the magnitude of the vector $ \| \vec{v} \| = \left(1,~1,~1\right) $ . | 1 |
| 3464 | Find the projection of the vector $ \vec{v_1} = \left(0,~\dfrac{ 6 }{ 5 },~\dfrac{ 3 }{ 5 }\right) $ on the vector $ \vec{v_2} = \left(-1,~1,~2\right) $. | 1 |
| 3465 | Calculate the cross product of the vectors $ \vec{v_1} = \left(11,~-1,~-2\right) $ and $ \vec{v_2} = \left(15,~-1,~-4\right) $ . | 1 |
| 3466 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-4,~3,~-5\right) $ and $ \vec{v_2} = \left(-8,~5,~3\right) $ . | 1 |
| 3467 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-13,~-3,~1\right) $ and $ \vec{v_2} = \left(-12,~1,~5\right) $ . | 1 |
| 3468 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~0,~3\right) $ and $ \vec{v_2} = \left(2,~3,~1\right) $ . | 1 |
| 3469 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-1,~2,~1\right) $ and $ \vec{v_2} = \left(1,~0,~-1\right) $ . | 1 |
| 3470 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-7,~3,~3\right) $ and $ \vec{v_2} = \left(-4,~3,~6\right) $ . | 1 |
| 3471 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~-1,~1\right) $ and $ \vec{v_2} = \left(0,~1,~1\right) $ . | 1 |
| 3472 | Find the projection of the vector $ \vec{v_1} = \left(1,~-1,~1\right) $ on the vector $ \vec{v_2} = \left(0,~1,~1\right) $. | 1 |
| 3473 | Calculate the dot product of the vectors $ \vec{v_1} = \left(0,~0,~6\right) $ and $ \vec{v_2} = \left(\dfrac{ 173 }{ 50 },~2,~0\right) $ . | 1 |
| 3474 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~4,~-4\right) $ and $ \vec{v_2} = \left(0,~3,~2\right) $ . | 1 |
| 3475 | Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~-2,~-5\right) $ and $ \vec{v_2} = \left(20,~-2,~3\right) $ . | 1 |
| 3476 | Find the magnitude of the vector $ \| \vec{v} \| = \left(5,~-7\right) $ . | 1 |
| 3477 | Find the angle between vectors $ \left(-4,~6\right)$ and $\left(6,~3\right)$. | 1 |
| 3478 | Find the magnitude of the vector $ \| \vec{v} \| = \left(0,~-4\right) $ . | 1 |
| 3479 | Find the angle between vectors $ \left(-11,~14\right)$ and $\left(20,~18\right)$. | 1 |
| 3480 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-5,~1\right) $ and $ \vec{v_2} = \left(2,~-5\right) $ . | 1 |
| 3481 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-9,~2,~6\right) $ and $ \vec{v_2} = \left(9,~7,~9\right) $ . | 1 |
| 3482 | Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~3,~2\right) $ and $ \vec{v_2} = \left(-24,~135,~-81\right) $ . | 1 |
| 3483 | Find the projection of the vector $ \vec{v_1} = \left(2,~6,~6\right) $ on the vector $ \vec{v_2} = \left(7,~9,~6\right) $. | 1 |
| 3484 | Calculate the cross product of the vectors $ \vec{v_1} = \left(5,~3,~0\right) $ and $ \vec{v_2} = \left(0,~3,~-1\right) $ . | 1 |
| 3485 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-5,~0\right) $ and $ \vec{v_2} = \left(9,~3\right) $ . | 1 |
| 3486 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-15,~-12\right) $ and $ \vec{v_2} = \left(-4,~5\right) $ . | 1 |
| 3487 | Calculate the dot product of the vectors $ \vec{v_1} = \left(0,~9\right) $ and $ \vec{v_2} = \left(-1,~-6\right) $ . | 1 |
| 3488 | Calculate the dot product of the vectors $ \vec{v_1} = \left(4,~-1\right) $ and $ \vec{v_2} = \left(12,~-3\right) $ . | 1 |
| 3489 | Find the magnitude of the vector $ \| \vec{v} \| = \left(0,~1\right) $ . | 1 |
| 3490 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-2,~-9\right) $ and $ \vec{v_2} = \left(-3,~-9\right) $ . | 1 |
| 3491 | Find the difference of the vectors $ \vec{v_1} = \left(0,~1\right) $ and $ \vec{v_2} = \left(-\dfrac{ 9 }{ 20 },~-\dfrac{ 9 }{ 20 }\right) $ . | 1 |
| 3492 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-9,~-5\right) $ and $ \vec{v_2} = \left(-3,~0\right) $ . | 1 |
| 3493 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-4,~1\right) $ and $ \vec{v_2} = \left(8,~-7\right) $ . | 1 |
| 3494 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-7,~-1\right) $ and $ \vec{v_2} = \left(8,~5\right) $ . | 1 |
| 3495 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-5,~-2\right) $ and $ \vec{v_2} = \left(-3,~-4\right) $ . | 1 |
| 3496 | Calculate the dot product of the vectors $ \vec{v_1} = \left(5,~\dfrac{ 20 }{ 3 }\right) $ and $ \vec{v_2} = \left(-4,~3\right) $ . | 1 |
| 3497 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~-6\right) $ and $ \vec{v_2} = \left(-9,~2\right) $ . | 1 |
| 3498 | Find the angle between vectors $ \left(8,~-9\right)$ and $\left(3,~-7\right)$. | 1 |
| 3499 | Find the angle between vectors $ \left(-7,~-4\right)$ and $\left(-7,~-9\right)$. | 1 |
| 3500 | Find the angle between vectors $ \left(-5,~-2\right)$ and $\left(-8,~-6\right)$. | 1 |
