Vectors
(the database of solved problems)
All the problems and solutions shown below were generated using the Vectors Calculator.
| ID |
Problem |
Count |
| 3501 | Find the angle between vectors $ \left(-5,~3\right)$ and $\left(5,~-3\right)$. | 1 |
| 3502 | Find the angle between vectors $ \left(-8,~-4\right)$ and $\left(0,~7\right)$. | 1 |
| 3503 | Find the angle between vectors $ \left(-8,~-3\right)$ and $\left(-4,~-8\right)$. | 1 |
| 3504 | Find the angle between vectors $ \left(1,~-6\right)$ and $\left(5,~-6\right)$. | 1 |
| 3505 | Calculate the cross product of the vectors $ \vec{v_1} = \left(5,~2,~2\right) $ and $ \vec{v_2} = \left(-1,~3,~1\right) $ . | 1 |
| 3506 | Find the sum of the vectors $ \vec{v_1} = \left(-242.8106,~-129.1047\right) $ and $ \vec{v_2} = \left(-\dfrac{ 153909 }{ 10000 },~\dfrac{ 422861 }{ 10000 }\right) $ . | 1 |
| 3507 | Calculate the cross product of the vectors $ \vec{v_1} = \left(2,~-3,~1\right) $ and $ \vec{v_2} = \left(-1,~-1,~-1\right) $ . | 1 |
| 3508 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-2,~3,~-1\right) $ and $ \vec{v_2} = \left(2,~1,~-1\right) $ . | 1 |
| 3509 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-2 \sqrt{ 6 },~5\right) $ . | 1 |
| 3510 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-5,~0\right) $ . | 1 |
| 3511 | Find the magnitude of the vector $ \| \vec{v} \| = \left(11,~0\right) $ . | 1 |
| 3512 | Find the magnitude of the vector $ \| \vec{v} \| = \left(11,~6\right) $ . | 1 |
| 3513 | Find the sum of the vectors $ \vec{v_1} = \left(24338,~0,~0\right) $ and $ \vec{v_2} = \left(0,~\dfrac{ 13667 }{ 200 },~0\right) $ . | 1 |
| 3514 | Find the sum of the vectors $ \vec{v_1} = \left(\dfrac{ 12169 }{ 500 },~0,~0\right) $ and $ \vec{v_2} = \left(0,~\dfrac{ 13667 }{ 200 },~0\right) $ . | 1 |
| 3515 | Find the angle between vectors $ \left(\dfrac{ 12169 }{ 500 },~0,~0\right)$ and $\left(0,~\dfrac{ 13667 }{ 200 },~0\right)$. | 1 |
| 3516 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-\dfrac{ 1 }{ 3 },~-\dfrac{ 3 }{ 2 }\right) $ . | 1 |
| 3517 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-2,~3\right) $ . | 1 |
| 3518 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~-6,~0\right) $ and $ \vec{v_2} = \left(2,~5,~3\right) $ . | 1 |
| 3519 | Calculate the dot product of the vectors $ \vec{v_1} = \left(92.5,~6.4\right) $ and $ \vec{v_2} = \left(5.3,~2.9\right) $ . | 1 |
| 3520 | Find the angle between vectors $ \left(-3,~8\right)$ and $\left(7,~-1\right)$. | 1 |
| 3521 | Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~0\right) $ and $ \vec{v_2} = \left(3,~0\right) $ . | 1 |
| 3522 | Find the sum of the vectors $ \vec{v_1} = \left(8,~1\right) $ and $ \vec{v_2} = \left(5,~-2\right) $ . | 1 |
| 3523 | Find the sum of the vectors $ \vec{v_1} = \left(-4,~0,~1\right) $ and $ \vec{v_2} = \left(1,~6,~-2\right) $ . | 1 |
| 3524 | Calculate the dot product of the vectors $ \vec{v_1} = \left(5,~6,~-7\right) $ and $ \vec{v_2} = \left(12,~-3,~-2\right) $ . | 1 |
| 3525 | Calculate the cross product of the vectors $ \vec{v_1} = \left(5,~6,~-7\right) $ and $ \vec{v_2} = \left(12,~-3,~-2\right) $ . | 1 |
| 3526 | Calculate the cross product of the vectors $ \vec{v_1} = \left(3,~5,~0\right) $ and $ \vec{v_2} = \left(0,~3,~-5\right) $ . | 1 |
| 3527 | Calculate the cross product of the vectors $ \vec{v_1} = \left(0,~3,~-5\right) $ and $ \vec{v_2} = \left(3,~5,~0\right) $ . | 1 |
| 3528 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-1,~0,~3\right) $ and $ \vec{v_2} = \left(2,~2,~1\right) $ . | 1 |
| 3529 | Calculate the cross product of the vectors $ \vec{v_1} = \left(3,~-1,~1\right) $ and $ \vec{v_2} = \left(0,~3,~-2\right) $ . | 1 |
| 3530 | Calculate the cross product of the vectors $ \vec{v_1} = \left(4,~-2,~1\right) $ and $ \vec{v_2} = \left(3,~-4,~1\right) $ . | 1 |
| 3531 | Calculate the dot product of the vectors $ \vec{v_1} = \left(3020,~280\right) $ and $ \vec{v_2} = \left(1,~1\right) $ . | 1 |
| 3532 | Calculate the dot product of the vectors $ \vec{v_1} = \left(3020,~2800\right) $ and $ \vec{v_2} = \left(1,~-1\right) $ . | 1 |
| 3533 | Find the projection of the vector $ \vec{v_1} = \left(-1,~3\right) $ on the vector $ \vec{v_2} = \left(4,~2\right) $. | 1 |
| 3534 | Find the sum of the vectors $ \vec{v_1} = \left(5,~0\right) $ and $ \vec{v_2} = \left(0,~12\right) $ . | 1 |
| 3535 | Determine whether the vectors $ \vec{v_1} = \left(-1,~-3\right) $ and $ \vec{v_2} = \left(2,~6\right) $ are linearly independent or dependent. | 1 |
| 3536 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-2,~-4\right) $ and $ \vec{v_2} = \left(4,~8\right) $ . | 1 |
| 3537 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~2,~3\right) $ and $ \vec{v_2} = \left(2,~-4,~-6\right) $ . | 1 |
| 3538 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~2,~3\right) $ and $ \vec{v_2} = \left(-1,~2,~3\right) $ . | 1 |
| 3539 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~2,~3\right) $ and $ \vec{v_2} = \left(-2,~4,~-8\right) $ . | 1 |
| 3540 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~2,~3\right) $ and $ \vec{v_2} = \left(1,~-2,~-3\right) $ . | 1 |
| 3541 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~2,~3\right) $ and $ \vec{v_2} = \left(-3,~6,~-9\right) $ . | 1 |
| 3542 | Find the projection of the vector $ \vec{v_1} = \left(-4,~3\right) $ on the vector $ \vec{v_2} = \left(8,~-6\right) $. | 1 |
| 3543 | Find the magnitude of the vector $ \| \vec{v} \| = \left(8,~\dfrac{ 248 }{ 25 }\right) $ . | 1 |
| 3544 | Calculate the cross product of the vectors $ \vec{v_1} = \left(5,~2,~-9\right) $ and $ \vec{v_2} = \left(-1,~1,~6\right) $ . | 1 |
| 3545 | Calculate the cross product of the vectors $ \vec{v_1} = \left(5,~2,~9\right) $ and $ \vec{v_2} = \left(-1,~1,~6\right) $ . | 1 |
| 3546 | Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~-39,~7\right) $ and $ \vec{v_2} = \left(3,~-5,~-5\right) $ . | 1 |
| 3547 | Determine whether the vectors $ \vec{v_1} = \left(4,~4,~2\right) $, $ \vec{v_2} = \left(-8,~6,~1\right) $ and $ \vec{v_3} = \left(3,~7,~-3\right)$ are linearly independent or dependent. | 1 |
| 3548 | Find the angle between vectors $ \left(8,~8,~9\right)$ and $\left(-8,~5,~7\right)$. | 1 |
| 3549 | Find the sum of the vectors $ \vec{v_1} = \left(-36,~30,~24\right) $ and $ \vec{v_2} = \left(-8,~40,~16\right) $ . | 1 |
| 3550 | Find the projection of the vector $ \vec{v_1} = \left(2,~6\right) $ on the vector $ \vec{v_2} = \left(1,~8\right) $. | 1 |
