Vectors
(the database of solved problems)
All the problems and solutions shown below were generated using the Vectors Calculator.
| ID |
Problem |
Count |
| 5851 | Find the magnitude of the vector $ \| \vec{v} \| = \left(4,~5\right) $ . | 1 |
| 5852 | Find the angle between vectors $ \left(1,~2,~3\right)$ and $\left(1,~1,~1\right)$. | 1 |
| 5853 | Find the angle between vectors $ \left(1,~-2,~2\right)$ and $\left(-3,~6,~2\right)$. | 1 |
| 5854 | Find the angle between vectors $ \left(1,~-2,~2\right)$ and $\left(4,~5,~3\right)$. | 1 |
| 5855 | Find the angle between vectors $ \left(1,~-2,~2\right)$ and $\left(-2,~4,~-4\right)$. | 1 |
| 5856 | Determine whether the vectors $ \vec{v_1} = \left(2,~1,~3\right) $, $ \vec{v_2} = \left(-3,~0,~1\right) $ and $ \vec{v_3} = \left(0,~0,~0\right)$ are linearly independent or dependent. | 1 |
| 5857 | Find the angle between vectors $ \left(2,~1,~3\right)$ and $\left(-3,~0,~1\right)$. | 1 |
| 5858 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~\dfrac{ 3 }{ 2 },~1\right) $ and $ \vec{v_2} = \left(0,~1,~2\right) $ . | 1 |
| 5859 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-1,~2,~0\right) $ and $ \vec{v_2} = \left(0,~1,~2\right) $ . | 1 |
| 5860 | Calculate the cross product of the vectors $ \vec{v_1} = \left(2,~-2,~1\right) $ and $ \vec{v_2} = \left(4,~2,~-1\right) $ . | 1 |
| 5861 | Find the difference of the vectors $ \vec{v_1} = \left(-27,~21\right) $ and $ \vec{v_2} = \left(-3,~1\right) $ . | 1 |
| 5862 | Find the sum of the vectors $ \vec{v_1} = \left(-1,~11,~10\right) $ and $ \vec{v_2} = \left(-8,~15,~14\right) $ . | 1 |
| 5863 | Calculate the dot product of the vectors $ \vec{v_1} = \left(4,~2\right) $ and $ \vec{v_2} = \left(1,~-2\right) $ . | 1 |
| 5864 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-45,~-55\right) $ . | 1 |
| 5865 | Find the projection of the vector $ \vec{v_1} = \left(-1,~11,~10\right) $ on the vector $ \vec{v_2} = \left(-8,~15,~14\right) $. | 1 |
| 5866 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~-4,~9\right) $ and $ \vec{v_2} = \left(-4,~3,~6\right) $ . | 1 |
| 5867 | Calculate the cross product of the vectors $ \vec{v_1} = \left(3,~4,~-2\right) $ and $ \vec{v_2} = \left(2,~-1,~2\right) $ . | 1 |
| 5868 | Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~4,~-2\right) $ and $ \vec{v_2} = \left(2,~-1,~2\right) $ . | 1 |
| 5869 | Find the angle between vectors $ \left(3,~4,~-2\right)$ and $\left(2,~-1,~2\right)$. | 1 |
| 5870 | Find the projection of the vector $ \vec{v_1} = \left(3,~4,~-2\right) $ on the vector $ \vec{v_2} = \left(2,~-1,~2\right) $. | 1 |
| 5871 | Find the magnitude of the vector $ \| \vec{v} \| = \left(2,~1,~1\right) $ . | 1 |
| 5872 | Calculate the cross product of the vectors $ \vec{v_1} = \left(2,~1,~1\right) $ and $ \vec{v_2} = \left(3,~-1,~2\right) $ . | 1 |
| 5873 | Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~-2,~4\right) $ and $ \vec{v_2} = \left(2,~\dfrac{ 5 }{ 2 },~0\right) $ . | 1 |
| 5874 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-1,~-2,~4\right) $ . | 1 |
| 5875 | Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~1,~-2\right) $ and $ \vec{v_2} = \left(-3,~-1,~0\right) $ . | 1 |
| 5876 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-1,~-2,~4\right) $ and $ \vec{v_2} = \left(-1,~3,~-2\right) $ . | 1 |
| 5877 | Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~2,~2\right) $ and $ \vec{v_2} = \left(0,~0,~-4\right) $ . | 1 |
| 5878 | Find the sum of the vectors $ \vec{v_1} = \left(0,~2,~3\right) $ and $ \vec{v_2} = \left(2,~3,~1\right) $ . | 1 |
| 5879 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-3,~5,~0\right) $ . | 1 |
| 5880 | Find the sum of the vectors $ \vec{v_1} = \left(2,~-3,~0\right) $ and $ \vec{v_2} = \left(-5,~4,~7\right) $ . | 1 |
| 5881 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~1,~-4\right) $ and $ \vec{v_2} = \left(2,~-1,~3\right) $ . | 1 |
| 5882 | Find the difference of the vectors $ \vec{v_1} = \left(-9,~9\right) $ and $ \vec{v_2} = \left(-1,~-5\right) $ . | 1 |
| 5883 | Find the magnitude of the vector $ \| \vec{v} \| = \left(3,~5\right) $ . | 1 |
| 5884 | Determine whether the vectors $ \vec{v_1} = \left(10,~-4,~6\right) $, $ \vec{v_2} = \left(-15,~6,~-9\right) $ and $ \vec{v_3} = \left(0,~0,~0\right)$ are linearly independent or dependent. | 1 |
| 5885 | Calculate the dot product of the vectors $ \vec{v_1} = \left(10,~-4,~6\right) $ and $ \vec{v_2} = \left(-15,~6,~-9\right) $ . | 1 |
| 5886 | Find the difference of the vectors $ \vec{v_1} = \left(1,~1\right) $ and $ \vec{v_2} = \left(0,~1\right) $ . | 1 |
| 5887 | Find the angle between vectors $ \left(1,~1\right)$ and $\left(0,~1\right)$. | 1 |
| 5888 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~1,~0\right) $ and $ \vec{v_2} = \left(1,~0,~0\right) $ . | 1 |
| 5889 | Calculate the cross product of the vectors $ \vec{v_1} = \left(0,~\dfrac{ 1 }{ 2 },~0\right) $ and $ \vec{v_2} = \left(1,~1,~0\right) $ . | 1 |
| 5890 | Calculate the cross product of the vectors $ \vec{v_1} = \left(0,~1,~0\right) $ and $ \vec{v_2} = \left(1,~0,~0\right) $ . | 1 |
| 5891 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-1,~1,~0\right) $ and $ \vec{v_2} = \left(1,~0,~0\right) $ . | 1 |
| 5892 | Find the magnitude of the vector $ \| \vec{v} \| = \left(1,~-1\right) $ . | 1 |
| 5893 | Find the magnitude of the vector $ \| \vec{v} \| = \left(0,~0,~0\right) $ . | 1 |
| 5894 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-5,~1,~2\right) $ and $ \vec{v_2} = \left(1,~0,~1\right) $ . | 1 |
| 5895 | Calculate the cross product of the vectors $ \vec{v_1} = \left(2,~-6,~-3\right) $ and $ \vec{v_2} = \left(4,~3,~-1\right) $ . | 1 |
| 5896 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~-4,~3\right) $ and $ \vec{v_2} = \left(3,~1,~-2\right) $ . | 1 |
| 5897 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~-4,~3\right) $ and $ \vec{v_2} = \left(3,~1,~-2\right) $ . | 1 |
| 5898 | Calculate the cross product of the vectors $ \vec{v_1} = \left(2,~6,~-2\right) $ and $ \vec{v_2} = \left(1,~1,~0\right) $ . | 1 |
| 5899 | Calculate the cross product of the vectors $ \vec{v_1} = \left(2,~6,~-1\right) $ and $ \vec{v_2} = \left(1,~1,~1\right) $ . | 1 |
| 5900 | Calculate the cross product of the vectors $ \vec{v_1} = \left(3,~4,~1\right) $ and $ \vec{v_2} = \left(1,~1,~1\right) $ . | 1 |
