Vectors
(the database of solved problems)
All the problems and solutions shown below were generated using the Vectors Calculator.
| ID |
Problem |
Count |
| 5551 | Find the magnitude of the vector $ \| \vec{v} \| = \left(4,~3,~5\right) $ . | 1 |
| 5552 | Find the magnitude of the vector $ \| \vec{v} \| = \left(0.0211,~0.0066\right) $ . | 1 |
| 5553 | Calculate the cross product of the vectors $ \vec{v_1} = \left(5,~-1,~6\right) $ and $ \vec{v_2} = \left(5,~-5,~-2\right) $ . | 1 |
| 5554 | Find the magnitude of the vector $ \| \vec{v} \| = \left(5,~-1,~6\right) $ . | 1 |
| 5555 | Find the sum of the vectors $ \vec{v_1} = \left(5,~-1,~6\right) $ and $ \vec{v_2} = \left(5,~-5,~-2\right) $ . | 1 |
| 5556 | Calculate the dot product of the vectors $ \vec{v_1} = \left(5,~-1,~6\right) $ and $ \vec{v_2} = \left(5,~-5,~-2\right) $ . | 1 |
| 5557 | Calculate the cross product of the vectors $ \vec{v_1} = \left(0,~50,~0\right) $ and $ \vec{v_2} = \left(-30,~0,~0\right) $ . | 1 |
| 5558 | Find the angle between vectors $ \left(12,~12\right)$ and $\left(0,~4\right)$. | 1 |
| 5559 | Calculate the dot product of the vectors $ \vec{v_1} = \left(12,~12\right) $ and $ \vec{v_2} = \left(0,~4\right) $ . | 1 |
| 5560 | Find the difference of the vectors $ \vec{v_1} = \left(0,~\dfrac{ 1041 }{ 1000 }\right) $ and $ \vec{v_2} = \left(0,~\dfrac{ 991 }{ 1000 }\right) $ . | 1 |
| 5561 | Find the magnitude of the vector $ \| \vec{v} \| = \left(4,~1\right) $ . | 1 |
| 5562 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-6,~-4\right) $ and $ \vec{v_2} = \left(-9,~-5\right) $ . | 1 |
| 5563 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-9,~-5\right) $ and $ \vec{v_2} = \left(-6,~-4\right) $ . | 1 |
| 5564 | Find the difference of the vectors $ \vec{v_1} = \left(3,~-3\right) $ and $ \vec{v_2} = \left(0,~-6\right) $ . | 1 |
| 5565 | Find the difference of the vectors $ \vec{v_1} = \left(3,~3\right) $ and $ \vec{v_2} = \left(-1,~1\right) $ . | 1 |
| 5566 | Find the magnitude of the vector $ \| \vec{v} \| = \left(5,~\dfrac{ 1 }{ 2 }\right) $ . | 1 |
| 5567 | Find the difference of the vectors $ \vec{v_1} = \left(5,~-3\right) $ and $ \vec{v_2} = \left(1,~2\right) $ . | 1 |
| 5568 | Find the magnitude of the vector $ \| \vec{v} \| = \left(7,~4\right) $ . | 1 |
| 5569 | Find the magnitude of the vector $ \| \vec{v} \| = \left(3,~4\right) $ . | 1 |
| 5570 | Calculate the cross product of the vectors $ \vec{v_1} = \left(2,~4,~-2\right) $ and $ \vec{v_2} = \left(6,~0,~10\right) $ . | 1 |
| 5571 | Find the magnitude of the vector $ \| \vec{v} \| = \left(13,~13\right) $ . | 1 |
| 5572 | Find the magnitude of the vector $ \| \vec{v} \| = \left(2,~3,~1\right) $ . | 1 |
| 5573 | Find the magnitude of the vector $ \| \vec{v} \| = \left(2,~3,~1\right) $ . | 1 |
| 5574 | Determine whether the vectors $ \vec{v_1} = \left(1,~2,~-2\right) $, $ \vec{v_2} = \left(1,~3,~1\right) $ and $ \vec{v_3} = \left(0,~0,~0\right)$ are linearly independent or dependent. | 1 |
| 5575 | Find the projection of the vector $ \vec{v_1} = \left(-6,~3\right) $ on the vector $ \vec{v_2} = \left(-1,~1\right) $. | 1 |
| 5576 | Find the sum of the vectors $ \vec{v_1} = \left(-5,~3\right) $ and $ \vec{v_2} = \left(-6,~8\right) $ . | 1 |
| 5577 | Find the difference of the vectors $ \vec{v_1} = \left(-8,~6\right) $ and $ \vec{v_2} = \left(-6,~2\right) $ . | 1 |
| 5578 | Find the difference of the vectors $ \vec{v_1} = \left(2,~-5\right) $ and $ \vec{v_2} = \left(-3,~-5\right) $ . | 1 |
| 5579 | Find the sum of the vectors $ \vec{v_1} = \left(2,~-5\right) $ and $ \vec{v_2} = \left(-3,~-5\right) $ . | 1 |
| 5580 | Find the difference of the vectors $ \vec{v_1} = \left(2,~-8\right) $ and $ \vec{v_2} = \left(7,~-7\right) $ . | 1 |
| 5581 | Find the sum of the vectors $ \vec{v_1} = \left(2,~-8\right) $ and $ \vec{v_2} = \left(7,~-7\right) $ . | 1 |
| 5582 | Find the sum of the vectors $ \vec{v_1} = \left(-2,~7\right) $ and $ \vec{v_2} = \left(1,~-3\right) $ . | 1 |
| 5583 | Find the sum of the vectors $ \vec{v_1} = \left(8,~1\right) $ and $ \vec{v_2} = \left(-7,~-1\right) $ . | 1 |
| 5584 | 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 |
| 5585 | Find the magnitude of the vector $ \| \vec{v} \| = \left(0,~0,~0\right) $ . | 1 |
| 5586 | Find the magnitude of the vector $ \| \vec{v} \| = \left(0,~-5,~1\right) $ . | 1 |
| 5587 | Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~4\right) $ and $ \vec{v_2} = \left(2,~-1\right) $ . | 1 |
| 5588 | Find the magnitude of the vector $ \| \vec{v} \| = \left(3,~4\right) $ . | 1 |
| 5589 | Find the projection of the vector $ \vec{v_1} = \left(3,~-6,~-1\right) $ on the vector $ \vec{v_2} = \left(1,~4,~-5\right) $. | 1 |
| 5590 | Find the magnitude of the vector $ \| \vec{v} \| = \left(0,~0\right) $ . | 1 |
| 5591 | Calculate the dot product of the vectors $ \vec{v_1} = \left(0,~0\right) $ and $ \vec{v_2} = \left(1347,~\dfrac{ 22269 }{ 125 }\right) $ . | 1 |
| 5592 | Find the sum of the vectors $ \vec{v_1} = \left(8,~6\right) $ and $ \vec{v_2} = \left(-3,~4\right) $ . | 1 |
| 5593 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-2,~3,~0\right) $ . | 1 |
| 5594 | Find the sum of the vectors $ \vec{v_1} = \left(-2,~3,~0\right) $ and $ \vec{v_2} = \left(0,~0,~6\right) $ . | 1 |
| 5595 | Calculate the cross product of the vectors $ \vec{v_1} = \left(2,~-1,~3\right) $ and $ \vec{v_2} = \left(1,~2,~5\right) $ . | 1 |
| 5596 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-3,~-1\right) $ . | 1 |
| 5597 | Find the projection of the vector $ \vec{v_1} = \left(3,~-1,~2\right) $ on the vector $ \vec{v_2} = \left(-5,~-2,~1\right) $. | 1 |
| 5598 | Find the angle between vectors $ \left(4,~4,~8\right)$ and $\left(2,~2,~1\right)$. | 1 |
| 5599 | Find the angle between vectors $ \left(0,~0,~3\right)$ and $\left(7,~0,~0\right)$. | 1 |
| 5600 | Calculate the cross product of the vectors $ \vec{v_1} = \left(0,~0,~3\right) $ and $ \vec{v_2} = \left(7,~0,~0\right) $ . | 1 |
