Vectors
(the database of solved problems)
All the problems and solutions shown below were generated using the Vectors Calculator.
| ID |
Problem |
Count |
| 6401 | Calculate the dot product of the vectors $ \vec{v_1} = \left(0,~0,~1\right) $ and $ \vec{v_2} = \left(0,~0,~1\right) $ . | 1 |
| 6402 | Calculate the cross product of the vectors $ \vec{v_1} = \left(0,~0,~1\right) $ and $ \vec{v_2} = \left(0,~0,~1\right) $ . | 1 |
| 6403 | Calculate the cross product of the vectors $ \vec{v_1} = \left(0,~0,~1\right) $ and $ \vec{v_2} = \left(0,~1,~0\right) $ . | 1 |
| 6404 | Find the projection of the vector $ \vec{v_1} = \left(0,~0,~1\right) $ on the vector $ \vec{v_2} = \left(0,~1,~0\right) $. | 1 |
| 6405 | Find the angle between vectors $ \left(6,~4\right)$ and $\left(5,~8\right)$. | 1 |
| 6406 | Find the sum of the vectors $ \vec{v_1} = \left(3,~8\right) $ and $ \vec{v_2} = \left(2,~9\right) $ . | 1 |
| 6407 | Find the sum of the vectors $ \vec{v_1} = \left(3,~4\right) $ and $ \vec{v_2} = \left(1,~1\right) $ . | 1 |
| 6408 | Find the difference of the vectors $ \vec{v_1} = \left(9,~0\right) $ and $ \vec{v_2} = \left(1,~4\right) $ . | 1 |
| 6409 | Find the sum of the vectors $ \vec{v_1} = \left(9,~0\right) $ and $ \vec{v_2} = \left(1,~4\right) $ . | 1 |
| 6410 | Find the difference of the vectors $ \vec{v_1} = \left(0,~0\right) $ and $ \vec{v_2} = \left(0,~3\right) $ . | 1 |
| 6411 | Find the sum of the vectors $ \vec{v_1} = \left(7,~-4\right) $ and $ \vec{v_2} = \left(-3,~-5\right) $ . | 1 |
| 6412 | Find the sum of the vectors $ \vec{v_1} = \left(4,~5\right) $ and $ \vec{v_2} = \left(-3,~5\right) $ . | 1 |
| 6413 | Find the sum of the vectors $ \vec{v_1} = \left(-3,~5\right) $ and $ \vec{v_2} = \left(4,~2\right) $ . | 1 |
| 6414 | Find the difference of the vectors $ \vec{v_1} = \left(-3,~5\right) $ and $ \vec{v_2} = \left(4,~2\right) $ . | 1 |
| 6415 | Find the sum of the vectors $ \vec{v_1} = \left(12,~27\right) $ and $ \vec{v_2} = \left(8,~0\right) $ . | 1 |
| 6416 | Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~-5\right) $ and $ \vec{v_2} = \left(-1,~5\right) $ . | 1 |
| 6417 | Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~-5\right) $ and $ \vec{v_2} = \left(-5,~4\right) $ . | 1 |
| 6418 | Calculate the dot product of the vectors $ \vec{v_1} = \left(8,~6\right) $ and $ \vec{v_2} = \left(-12,~16\right) $ . | 1 |
| 6419 | Find the angle between vectors $ \left(4,~-5\right)$ and $\left(-5,~2\right)$. | 1 |
| 6420 | Find the angle between vectors $ \left(-6,~3\right)$ and $\left(6,~2\right)$. | 1 |
| 6421 | Find the angle between vectors $ \left(3,~2\right)$ and $\left(9,~6\right)$. | 1 |
| 6422 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~2,~3\right) $ and $ \vec{v_2} = \left(5,~-4,~-3\right) $ . | 1 |
| 6423 | Calculate the cross product of the vectors $ \vec{v_1} = \left(2,~-1,~5\right) $ and $ \vec{v_2} = \left(3,~2,~-1\right) $ . | 1 |
| 6424 | Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~-1,~5\right) $ and $ \vec{v_2} = \left(3,~2,~-1\right) $ . | 1 |
| 6425 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-2,~2,~2\right) $ . | 1 |
| 6426 | Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~1,~-4\right) $ and $ \vec{v_2} = \left(-5,~2,~7\right) $ . | 1 |
| 6427 | Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~1,~-4\right) $ and $ \vec{v_2} = \left(-5,~-2,~7\right) $ . | 1 |
| 6428 | Find the angle between vectors $ \left(1,~2\right)$ and $\left(1,~-3\right)$. | 1 |
| 6429 | Calculate the cross product of the vectors $ \vec{v_1} = \left(3,~7,~-6\right) $ and $ \vec{v_2} = \left(2,~1,~-2\right) $ . | 1 |
| 6430 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-5,~4,~12\right) $ and $ \vec{v_2} = \left(3,~4,~4\right) $ . | 1 |
| 6431 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-32,~56,~32\right) $ . | 1 |
| 6432 | Find the difference of the vectors $ \vec{v_1} = \left(0,~-16\right) $ and $ \vec{v_2} = \left(12,~-20\right) $ . | 1 |
| 6433 | Find the angle between vectors $ \left(0.1534,~-0.8874,~0.4347\right)$ and $\left(-0.3783,~-0.5898,~0.7134\right)$. | 1 |
| 6434 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-3,~3,~0\right) $ and $ \vec{v_2} = \left(-6,~0,~0\right) $ . | 1 |
| 6435 | Calculate the dot product of the vectors $ \vec{v_1} = \left(0,~0,~18\right) $ and $ \vec{v_2} = \left(0,~0,~3\right) $ . | 1 |
| 6436 | Find the sum of the vectors $ \vec{v_1} = \left(2,~6\right) $ and $ \vec{v_2} = \left(-1,~-4\right) $ . | 1 |
| 6437 | Find the sum of the vectors $ \vec{v_1} = \left(-3,~2\right) $ and $ \vec{v_2} = \left(-6,~6\right) $ . | 1 |
| 6438 | Find the magnitude of the vector $ \| \vec{v} \| = \left(10,~10,~1\right) $ . | 1 |
| 6439 | Find the angle between vectors $ \left(2,~2,~0\right)$ and $\left(0,~0,~18\right)$. | 1 |
| 6440 | Determine whether the vectors $ \vec{v_1} = \left(1,~2,~1\right) $, $ \vec{v_2} = \left(1,~0,~1\right) $ and $ \vec{v_3} = \left(0,~0,~0\right)$ are linearly independent or dependent. | 1 |
| 6441 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~0,~0\right) $ and $ \vec{v_2} = \left(0,~1,~0\right) $ . | 1 |
| 6442 | Calculate the dot product of the vectors $ \vec{v_1} = \left(0,~0,~-1\right) $ and $ \vec{v_2} = \left(0,~0,~-1\right) $ . | 1 |
| 6443 | Find the angle between vectors $ \left(1,~-1\right)$ and $\left(4,~5\right)$. | 1 |
| 6444 | Find the magnitude of the vector $ \| \vec{v} \| = \left(0,~40\right) $ . | 1 |
| 6445 | Find the sum of the vectors $ \vec{v_1} = \left(4,~8\right) $ and $ \vec{v_2} = \left(10,~10\right) $ . | 1 |
| 6446 | Find the difference of the vectors $ \vec{v_1} = \left(4,~8\right) $ and $ \vec{v_2} = \left(10,~10\right) $ . | 1 |
| 6447 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-4,~-1,~-4\right) $ and $ \vec{v_2} = \left(4,~-1,~-4\right) $ . | 1 |
| 6448 | Calculate the cross product of the vectors $ \vec{v_1} = \left(2,~4,~-2\right) $ and $ \vec{v_2} = \left(3,~1,~3\right) $ . | 1 |
| 6449 | Calculate the cross product of the vectors $ \vec{v_1} = \left(4,~3,~-1\right) $ and $ \vec{v_2} = \left(-3,~0,~-1\right) $ . | 1 |
| 6450 | Find the difference of the vectors $ \vec{v_1} = \left(4,~-3,~-22\right) $ and $ \vec{v_2} = \left(0,~0,~0\right) $ . | 1 |
