Vectors
(the database of solved problems)
All the problems and solutions shown below were generated using the Vectors Calculator.
| ID |
Problem |
Count |
| 3801 | Calculate the dot product of the vectors $ \vec{v_1} = \left(0,~5,~3\right) $ and $ \vec{v_2} = \left(4,~1,~0\right) $ . | 1 |
| 3802 | Calculate the dot product of the vectors $ \vec{v_1} = \left(0,~5,~3\right) $ and $ \vec{v_2} = \left(-8,~-1,~0\right) $ . | 1 |
| 3803 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-1,~0,~0\right) $ . | 1 |
| 3804 | Find the angle between vectors $ \left(-1,~1,~-1\right)$ and $\left(1,~-1,~1\right)$. | 1 |
| 3805 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-4,~-3,~2\right) $ . | 1 |
| 3806 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-\dfrac{ 2 }{ 5 },~3,~\dfrac{ 7 }{ 5 }\right) $ . | 1 |
| 3807 | Determine whether the vectors $ \vec{v_1} = \left(2,~-1\right) $ and $ \vec{v_2} = \left(1,~-2\right) $ are linearly independent or dependent. | 1 |
| 3808 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~2,~-7\right) $ and $ \vec{v_2} = \left(5,~1,~1\right) $ . | 1 |
| 3809 | Find the magnitude of the vector $ \| \vec{v} \| = \left(9,~-36,~-9\right) $ . | 1 |
| 3810 | Find the magnitude of the vector $ \| \vec{v} \| = \left(300,~0,~0\right) $ . | 1 |
| 3811 | Find the magnitude of the vector $ \| \vec{v} \| = \left(300,~300,~300\right) $ . | 1 |
| 3812 | Find the angle between vectors $ \left(1,~3\right)$ and $\left(-3,~1\right)$. | 1 |
| 3813 | Find the magnitude of the vector $ \| \vec{v} \| = \left(1,~2,~0\right) $ . | 1 |
| 3814 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~2,~0\right) $ and $ \vec{v_2} = \left(1,~-4,~-1\right) $ . | 1 |
| 3815 | Calculate the cross product of the vectors $ \vec{v_1} = \left(0,~0,~-1\right) $ and $ \vec{v_2} = \left(-1,~-4,~-1\right) $ . | 1 |
| 3816 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-4,~1,~0\right) $ . | 1 |
| 3817 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~1,~1\right) $ and $ \vec{v_2} = \left(-1,~-1,~-1\right) $ . | 1 |
| 3818 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~1,~1\right) $ and $ \vec{v_2} = \left(1,~-1,~0\right) $ . | 1 |
| 3819 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~0,~1\right) $ and $ \vec{v_2} = \left(1,~2,~3\right) $ . | 1 |
| 3820 | Calculate the cross product of the vectors $ \vec{v_1} = \left(0,~0,~-1\right) $ and $ \vec{v_2} = \left(1,~-4,~-1\right) $ . | 1 |
| 3821 | Calculate the cross product of the vectors $ \vec{v_1} = \left(2,~2,~1\right) $ and $ \vec{v_2} = \left(3,~1,~3\right) $ . | 1 |
| 3822 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~1,~2\right) $ and $ \vec{v_2} = \left(1,~-1,~0\right) $ . | 1 |
| 3823 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~1,~2\right) $ and $ \vec{v_2} = \left(1,~-1,~0\right) $ . | 1 |
| 3824 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~0,~0\right) $ and $ \vec{v_2} = \left(-1,~1,~0\right) $ . | 1 |
| 3825 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~0,~0\right) $ and $ \vec{v_2} = \left(0,~1,~2\right) $ . | 1 |
| 3826 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~0,~0\right) $ and $ \vec{v_2} = \left(0,~1,~2\right) $ . | 1 |
| 3827 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~1,~0\right) $ and $ \vec{v_2} = \left(1,~0,~-1\right) $ . | 1 |
| 3828 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~1,~0\right) $ and $ \vec{v_2} = \left(1,~0,~-2\right) $ . | 1 |
| 3829 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~1,~0\right) $ and $ \vec{v_2} = \left(-1,~0,~-2\right) $ . | 1 |
| 3830 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~1,~0\right) $ and $ \vec{v_2} = \left(-1,~0,~0\right) $ . | 1 |
| 3831 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~1,~0\right) $ and $ \vec{v_2} = \left(-1,~0,~1\right) $ . | 1 |
| 3832 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~1,~0\right) $ and $ \vec{v_2} = \left(-1,~1,~1\right) $ . | 1 |
| 3833 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~1,~0\right) $ and $ \vec{v_2} = \left(-1,~1,~1\right) $ . | 1 |
| 3834 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~-2,~1\right) $ and $ \vec{v_2} = \left(3,~2,~1\right) $ . | 1 |
| 3835 | Find the angle between vectors $ \left(-1,~3,~2\right)$ and $\left(1,~-3,~-2\right)$. | 1 |
| 3836 | Find the magnitude of the vector $ \| \vec{v} \| = \left(5,~8\right) $ . | 1 |
| 3837 | Find the sum of the vectors $ \vec{v_1} = \left(3,~1\right) $ and $ \vec{v_2} = \left(6,~-4\right) $ . | 1 |
| 3838 | Find the magnitude of the vector $ \| \vec{v} \| = \left(1723,~0\right) $ . | 1 |
| 3839 | Find the magnitude of the vector $ \| \vec{v} \| = \left(1,~2,~3\right) $ . | 1 |
| 3840 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~2,~3\right) $ and $ \vec{v_2} = \left(2,~1,~3\right) $ . | 1 |
| 3841 | Find the angle between vectors $ \left(1,~2,~3\right)$ and $\left(2,~1,~3\right)$. | 1 |
| 3842 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~2,~3\right) $ and $ \vec{v_2} = \left(2,~1,~3\right) $ . | 1 |
| 3843 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-0.3333,~-1.5\right) $ and $ \vec{v_2} = \left(2,~9\right) $ . | 1 |
| 3844 | Find the angle between vectors $ \left(-1,~2\right)$ and $\left(2,~1\right)$. | 1 |
| 3845 | Calculate the dot product of the vectors $ \vec{v_1} = \left(9,~309\right) $ and $ \vec{v_2} = \left(0,~0\right) $ . | 1 |
| 3846 | Find the magnitude of the vector $ \| \vec{v} \| = \left(3,~2,~7\right) $ . | 1 |
| 3847 | Calculate the cross product of the vectors $ \vec{v_1} = \left(31,~-22,~39\right) $ and $ \vec{v_2} = \left(40,~17,~46\right) $ . | 1 |
| 3848 | Calculate the cross product of the vectors $ \vec{v_1} = \left(7,~-7,~9\right) $ and $ \vec{v_2} = \left(9,~4,~-10\right) $ . | 1 |
| 3849 | Calculate the cross product of the vectors $ \vec{v_1} = \left(2,~6,~4\right) $ and $ \vec{v_2} = \left(1,~-2,~8\right) $ . | 1 |
| 3850 | Find the angle between vectors $ \left(2,~3\right)$ and $\left(4,~6\right)$. | 1 |
