Vectors
(the database of solved problems)
All the problems and solutions shown below were generated using the Vectors Calculator.
| ID |
Problem |
Count |
| 6501 | Calculate the dot product of the vectors $ \vec{v_1} = \left(5,~-12\right) $ and $ \vec{v_2} = \left(15,~8\right) $ . | 1 |
| 6502 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~1,~0\right) $ and $ \vec{v_2} = \left(1,~0,~2\right) $ . | 1 |
| 6503 | Find the difference of the vectors $ \vec{v_1} = \left(5,~-12\right) $ and $ \vec{v_2} = \left(15,~8\right) $ . | 1 |
| 6504 | Find the projection of the vector $ \vec{v_1} = \left(7,~0\right) $ on the vector $ \vec{v_2} = \left(9,~0\right) $. | 1 |
| 6505 | Find the difference of the vectors $ \vec{v_1} = \left(-2,~-4,~3\right) $ and $ \vec{v_2} = \left(3,~-1,~-2\right) $ . | 1 |
| 6506 | Calculate the dot product of the vectors $ \vec{v_1} = \left(6,~-6\right) $ and $ \vec{v_2} = \left(4,~5\right) $ . | 1 |
| 6507 | Find the projection of the vector $ \vec{v_1} = \left(4,~-5\right) $ on the vector $ \vec{v_2} = \left(3,~-1\right) $. | 1 |
| 6508 | Find the angle between vectors $ \left(4,~3\right)$ and $\left(-1,~5\right)$. | 1 |
| 6509 | Find the magnitude of the vector $ \| \vec{v} \| = \left(0,~0\right) $ . | 1 |
| 6510 | Find the projection of the vector $ \vec{v_1} = \left(5,~-4,~-5\right) $ on the vector $ \vec{v_2} = \left(2,~-1,~5\right) $. | 1 |
| 6511 | Find the projection of the vector $ \vec{v_1} = \left(2,~-1,~5\right) $ on the vector $ \vec{v_2} = \left(5,~-4,~-5\right) $. | 1 |
| 6512 | Determine whether the vectors $ \vec{v_1} = \left(15,~-8\right) $ and $ \vec{v_2} = \left(-5,~12\right) $ are linearly independent or dependent. | 1 |
| 6513 | Calculate the dot product of the vectors $ \vec{v_1} = \left(15,~-8\right) $ and $ \vec{v_2} = \left(-5,~12\right) $ . | 1 |
| 6514 | Find the angle between vectors $ \left(15,~-8\right)$ and $\left(-5,~12\right)$. | 1 |
| 6515 | Find the sum of the vectors $ \vec{v_1} = \left(3,~-1\right) $ and $ \vec{v_2} = \left(12,~15\right) $ . | 1 |
| 6516 | Find the difference of the vectors $ \vec{v_1} = \left(3,~-1\right) $ and $ \vec{v_2} = \left(12,~15\right) $ . | 1 |
| 6517 | Find the angle between vectors $ \left(5,~5\right)$ and $\left(-8,~8\right)$. | 1 |
| 6518 | Find the difference of the vectors $ \vec{v_1} = \left(2,~4\right) $ and $ \vec{v_2} = \left(4,~3\right) $ . | 1 |
| 6519 | Calculate the dot product of the vectors $ \vec{v_1} = \left(5,~3\right) $ and $ \vec{v_2} = \left(3,~-5\right) $ . | 1 |
| 6520 | Find the magnitude of the vector $ \| \vec{v} \| = \left(2,~1\right) $ . | 1 |
| 6521 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-2,~-3,~0\right) $ and $ \vec{v_2} = \left(4,~-1,~0\right) $ . | 1 |
| 6522 | Find the magnitude of the vector $ \| \vec{v} \| = \left(0,~2,~-5\right) $ . | 1 |
| 6523 | Find the magnitude of the vector $ \| \vec{v} \| = \left(0,~6\right) $ . | 1 |
| 6524 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~2\right) $ and $ \vec{v_2} = \left(-1,~1\right) $ . | 1 |
| 6525 | Determine whether the vectors $ \vec{v_1} = \left(2,~1,~2\right) $, $ \vec{v_2} = \left(1,~2,~1\right) $ and $ \vec{v_3} = \left(0,~1,~1\right)$ are linearly independent or dependent. | 1 |
| 6526 | Find the magnitude of the vector $ \| \vec{v} \| = \left(1,~2,~2\right) $ . | 1 |
| 6527 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~2,~-1\right) $ and $ \vec{v_2} = \left(2,~1,~4\right) $ . | 1 |
| 6528 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-1,~0,~3\right) $ and $ \vec{v_2} = \left(1,~2,~-1\right) $ . | 1 |
| 6529 | Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~-1,~4\right) $ and $ \vec{v_2} = \left(0,~3,~-1\right) $ . | 1 |
| 6530 | Find the difference of the vectors $ \vec{v_1} = \left(1,~2,~3\right) $ and $ \vec{v_2} = \left(1,~-1,~4\right) $ . | 1 |
| 6531 | Calculate the dot product of the vectors $ \vec{v_1} = \left(4,~2\right) $ and $ \vec{v_2} = \left(2,~4\right) $ . | 1 |
| 6532 | Find the difference of the vectors $ \vec{v_1} = \left(4,~2\right) $ and $ \vec{v_2} = \left(2,~4\right) $ . | 1 |
| 6533 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-2,~3,~1\right) $ and $ \vec{v_2} = \left(-2,~5,~0\right) $ . | 1 |
| 6534 | Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~3,~-1\right) $ and $ \vec{v_2} = \left(-3,~0,~0\right) $ . | 1 |
| 6535 | Find the magnitude of the vector $ \| \vec{v} \| = \left(6,~-2\right) $ . | 1 |
| 6536 | Find the sum of the vectors $ \vec{v_1} = \left(4,~-7\right) $ and $ \vec{v_2} = \left(5,~1\right) $ . | 1 |
| 6537 | Find the angle between vectors $ \left(-1,~3\right)$ and $\left(5,~5\right)$. | 1 |
| 6538 | Find the magnitude of the vector $ \| \vec{v} \| = \left(9,~-9\right) $ . | 1 |
| 6539 | Find the magnitude of the vector $ \| \vec{v} \| = \left(4,~-8\right) $ . | 1 |
| 6540 | Find the difference of the vectors $ \vec{v_1} = \left(-2,~3,~-1\right) $ and $ \vec{v_2} = \left(2,~1,~3\right) $ . | 1 |
| 6541 | Find the difference of the vectors $ \vec{v_1} = \left(1,~-2\right) $ and $ \vec{v_2} = \left(5,~-4\right) $ . | 1 |
| 6542 | Find the magnitude of the vector $ \| \vec{v} \| = \left(4,~-7\right) $ . | 1 |
| 6543 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-2,~-1\right) $ and $ \vec{v_2} = \left(2,~1\right) $ . | 1 |
| 6544 | Calculate the dot product of the vectors $ \vec{v_1} = \left(\dfrac{ 3 }{ 10 },~-\dfrac{ 2 }{ 5 },~0\right) $ and $ \vec{v_2} = \left(0,~0,~\dfrac{ 1 }{ 10 }\right) $ . | 1 |
| 6545 | Find the magnitude of the vector $ \| \vec{v} \| = \left(0,~0,~0\right) $ . | 1 |
| 6546 | Calculate the cross product of the vectors $ \vec{v_1} = \left(\dfrac{ 3 }{ 10 },~-\dfrac{ 2 }{ 5 },~0\right) $ and $ \vec{v_2} = \left(0,~0,~\dfrac{ 1 }{ 10 }\right) $ . | 1 |
| 6547 | Determine whether the vectors $ \vec{v_1} = \left(1,~4,~-2\right) $, $ \vec{v_2} = \left(6,~-2,~8\right) $ and $ \vec{v_3} = \left(0,~0,~0\right)$ are linearly independent or dependent. | 1 |
| 6548 | Calculate the dot product of the vectors $ \vec{v_1} = \left(5,~5\right) $ and $ \vec{v_2} = \left(-6,~1\right) $ . | 1 |
| 6549 | Find the sum of the vectors $ \vec{v_1} = \left(-7,~1\right) $ and $ \vec{v_2} = \left(-5,~8\right) $ . | 1 |
| 6550 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~-1,~1\right) $ and $ \vec{v_2} = \left(3,~4,~2\right) $ . | 1 |
