Vectors
(the database of solved problems)
All the problems and solutions shown below were generated using the Vectors Calculator.
| ID |
Problem |
Count |
| 5801 | Find the angle between vectors $ \left(5,~5,~1\right)$ and $\left(2,~1,~-1\right)$. | 1 |
| 5802 | Find the sum of the vectors $ \vec{v_1} = \left(6,~4\right) $ and $ \vec{v_2} = \left(-1,~4\right) $ . | 1 |
| 5803 | Find the magnitude of the vector $ \| \vec{v} \| = \left(3,~-1,~2\right) $ . | 1 |
| 5804 | Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~5,~4\right) $ and $ \vec{v_2} = \left(0,~2,~2\right) $ . | 1 |
| 5805 | Calculate the cross product of the vectors $ \vec{v_1} = \left(2,~5,~4\right) $ and $ \vec{v_2} = \left(0,~2,~2\right) $ . | 1 |
| 5806 | Find the angle between vectors $ \left(2,~5,~4\right)$ and $\left(0,~2,~2\right)$. | 1 |
| 5807 | Find the magnitude of the vector $ \| \vec{v} \| = \left(3,~2\right) $ . | 1 |
| 5808 | Find the angle between vectors $ \left(4,~3\right)$ and $\left(5,~-12\right)$. | 1 |
| 5809 | Find the sum of the vectors $ \vec{v_1} = \left(-7,~-1\right) $ and $ \vec{v_2} = \left(2,~2\right) $ . | 1 |
| 5810 | Find the magnitude of the vector $ \| \vec{v} \| = \left(24.35,~173.29\right) $ . | 1 |
| 5811 | Find the magnitude of the vector $ \| \vec{v} \| = \left(24.35,~173.29\right) $ . | 1 |
| 5812 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-7,~-6,~9\right) $ . | 1 |
| 5813 | Find the magnitude of the vector $ \| \vec{v} \| = \left(0,~10\right) $ . | 1 |
| 5814 | Calculate the dot product of the vectors $ \vec{v_1} = \left(8,~4\right) $ and $ \vec{v_2} = \left(-6,~5\right) $ . | 1 |
| 5815 | Calculate the dot product of the vectors $ \vec{v_1} = \left(6,~10\right) $ and $ \vec{v_2} = \left(-1,~5\right) $ . | 1 |
| 5816 | Find the angle between vectors $ \left(1,~0\right)$ and $\left(0,~-5\right)$. | 1 |
| 5817 | Find the magnitude of the vector $ \| \vec{v} \| = \left(1,~2,~3\right) $ . | 1 |
| 5818 | Find the sum of the vectors $ \vec{v_1} = \left(3,~5\right) $ and $ \vec{v_2} = \left(6,~8\right) $ . | 1 |
| 5819 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-6,~4\right) $ . | 1 |
| 5820 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-6,~4\right) $ and $ \vec{v_2} = \left(-3,~2\right) $ . | 1 |
| 5821 | Find the projection of the vector $ \vec{v_1} = \left(-6,~4\right) $ on the vector $ \vec{v_2} = \left(-3,~2\right) $. | 1 |
| 5822 | Determine whether the vectors $ \vec{v_1} = \left(15,~30\right) $ and $ \vec{v_2} = \left(-1,~4\right) $ are linearly independent or dependent. | 1 |
| 5823 | Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~3,~3\right) $ and $ \vec{v_2} = \left(6,~6,~6\right) $ . | 1 |
| 5824 | Find the magnitude of the vector $ \| \vec{v} \| = \left(3,~3,~3\right) $ . | 1 |
| 5825 | Find the angle between vectors $ \left(-3,~5,~1\right)$ and $\left(-9,~-2,~5\right)$. | 1 |
| 5826 | Find the angle between vectors $ \left(3,~5,~1\right)$ and $\left(-9,~2,~5\right)$. | 1 |
| 5827 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-3,~5,~1\right) $ and $ \vec{v_2} = \left(-9,~-2,~5\right) $ . | 1 |
| 5828 | Find the magnitude of the vector $ \| \vec{v} \| = \left(1,~-2,~3\right) $ . | 1 |
| 5829 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~-2,~3\right) $ and $ \vec{v_2} = \left(5,~0,~2\right) $ . | 1 |
| 5830 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~-2,~3\right) $ and $ \vec{v_2} = \left(5,~0,~2\right) $ . | 1 |
| 5831 | Find the sum of the vectors $ \vec{v_1} = \left(1,~-2,~3\right) $ and $ \vec{v_2} = \left(5,~0,~2\right) $ . | 1 |
| 5832 | Find the difference of the vectors $ \vec{v_1} = \left(1,~-2,~3\right) $ and $ \vec{v_2} = \left(5,~0,~2\right) $ . | 1 |
| 5833 | Find the angle between vectors $ \left(1,~-2,~3\right)$ and $\left(5,~0,~2\right)$. | 1 |
| 5834 | Determine whether the vectors $ \vec{v_1} = \left(1,~-2,~3\right) $, $ \vec{v_2} = \left(5,~0,~2\right) $ and $ \vec{v_3} = \left(1,~-1,~3\right)$ are linearly independent or dependent. | 1 |
| 5835 | Calculate the cross product of the vectors $ \vec{v_1} = \left(3,~-1,~1\right) $ and $ \vec{v_2} = \left(-3,~3,~-2\right) $ . | 1 |
| 5836 | Calculate the dot product of the vectors $ \vec{v_1} = \left(7,~5,~-4\right) $ and $ \vec{v_2} = \left(-1,~3,~6\right) $ . | 1 |
| 5837 | Calculate the cross product of the vectors $ \vec{v_1} = \left(4,~-2,~2\right) $ and $ \vec{v_2} = \left(1,~0,~1\right) $ . | 1 |
| 5838 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-2,~-2,~2\right) $ and $ \vec{v_2} = \left(-2,~2,~-8\right) $ . | 1 |
| 5839 | Calculate the cross product of the vectors $ \vec{v_1} = \left(7,~-5,~8\right) $ and $ \vec{v_2} = \left(-8,~6,~-9\right) $ . | 1 |
| 5840 | Calculate the cross product of the vectors $ \vec{v_1} = \left(6,~7,~-1\right) $ and $ \vec{v_2} = \left(-3,~-1,~2\right) $ . | 1 |
| 5841 | Calculate the cross product of the vectors $ \vec{v_1} = \left(4,~-4,~3\right) $ and $ \vec{v_2} = \left(3,~2,~3\right) $ . | 1 |
| 5842 | Calculate the cross product of the vectors $ \vec{v_1} = \left(2,~-2,~3\right) $ and $ \vec{v_2} = \left(-6,~0,~-5\right) $ . | 1 |
| 5843 | Find the magnitude of the vector $ \| \vec{v} \| = \left(2,~4,~6\right) $ . | 1 |
| 5844 | Find the angle between vectors $ \left(2,~4,~6\right)$ and $\left(1,~3,~7\right)$. | 1 |
| 5845 | Find the magnitude of the vector $ \| \vec{v} \| = \left(3,~-7\right) $ . | 1 |
| 5846 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~-6,~-4\right) $ and $ \vec{v_2} = \left(1,~-2,~-8\right) $ . | 1 |
| 5847 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~2,~4\right) $ and $ \vec{v_2} = \left(-1,~3,~6\right) $ . | 1 |
| 5848 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-8,~-8,~1\right) $ and $ \vec{v_2} = \left(7,~0,~3\right) $ . | 1 |
| 5849 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-2,~-5\right) $ . | 1 |
| 5850 | Find the magnitude of the vector $ \| \vec{v} \| = \left(5,~8\right) $ . | 1 |
