Vectors
(the database of solved problems)
All the problems and solutions shown below were generated using the Vectors Calculator.
| ID |
Problem |
Count |
| 3851 | Find the angle between vectors $ \left(3,~7\right)$ and $\left(9,~22\right)$. | 1 |
| 3852 | Find the sum of the vectors $ \vec{v_1} = \left(0,~0\right) $ and $ \vec{v_2} = \left(1,~2\right) $ . | 1 |
| 3853 | Find the magnitude of the vector $ \| \vec{v} \| = \left(0,~0\right) $ . | 1 |
| 3854 | Find the projection of the vector $ \vec{v_1} = \left(0,~0\right) $ on the vector $ \vec{v_2} = \left(1,~2\right) $. | 1 |
| 3855 | Find the magnitude of the vector $ \| \vec{v} \| = \left(1,~2\right) $ . | 1 |
| 3856 | Calculate the dot product of the vectors $ \vec{v_1} = \left(39,~23,~-13\right) $ and $ \vec{v_2} = \left(8,~-13,~1\right) $ . | 1 |
| 3857 | Find the angle between vectors $ \left(39,~23,~-13\right)$ and $\left(8,~-13,~1\right)$. | 1 |
| 3858 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-\dfrac{ 3 }{ 2 },~\dfrac{ 19 }{ 2 },~-13\right) $ and $ \vec{v_2} = \left(-\dfrac{ 11 }{ 2 },~\dfrac{ 1 }{ 2 },~1\right) $ . | 1 |
| 3859 | Find the angle between vectors $ \left(-\dfrac{ 3 }{ 2 },~\dfrac{ 19 }{ 2 },~-13\right)$ and $\left(-\dfrac{ 11 }{ 2 },~\dfrac{ 1 }{ 2 },~1\right)$. | 1 |
| 3860 | Calculate the cross product of the vectors $ \vec{v_1} = \left(2,~2,~-1\right) $ and $ \vec{v_2} = \left(-1,~3,~4\right) $ . | 1 |
| 3861 | Calculate the cross product of the vectors $ \vec{v_1} = \left(2,~2,~-1\right) $ and $ \vec{v_2} = \left(1,~1,~1\right) $ . | 1 |
| 3862 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-1,~3,~4\right) $ and $ \vec{v_2} = \left(1,~1,~1\right) $ . | 1 |
| 3863 | Calculate the dot product of the vectors $ \vec{v_1} = \left(3.9,~-1.5\right) $ and $ \vec{v_2} = \left(0,~0\right) $ . | 1 |
| 3864 | Calculate the cross product of the vectors $ \vec{v_1} = \left(3,~2,~1\right) $ and $ \vec{v_2} = \left(1,~1,~-1\right) $ . | 1 |
| 3865 | Determine whether the vectors $ \vec{v_1} = \left(1,~2\right) $ and $ \vec{v_2} = \left(4,~8\right) $ are linearly independent or dependent. | 1 |
| 3866 | Find the angle between vectors $ \left(28,~49,~-30\right)$ and $\left(-20,~-50,~-30\right)$. | 1 |
| 3867 | Find the magnitude of the vector $ \| \vec{v} \| = \left(2,~9,~3\right) $ . | 1 |
| 3868 | Find the angle between vectors $ \left(28,~49,~-30\right)$ and $\left(0,~0,~-30\right)$. | 1 |
| 3869 | Find the angle between vectors $ \left(8,~20,~12\right)$ and $\left(28,~49,~-30\right)$. | 1 |
| 3870 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-3,~3,~2\right) $ and $ \vec{v_2} = \left(-2,~-1,~-5\right) $ . | 1 |
| 3871 | Find the angle between vectors $ \left(-\dfrac{ 382651 }{ 20000 },~6.9544,~\dfrac{ 4824211 }{ 100000 }\right)$ and $\left(-\dfrac{ 3755677 }{ 100000 },~\dfrac{ 9116101 }{ 100000 },~0.5461\right)$. | 1 |
| 3872 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-3,~3,~2\right) $ and $ \vec{v_2} = \left(-4,~5,~5\right) $ . | 1 |
| 3873 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-3,~3,~2\right) $ and $ \vec{v_2} = \left(-2,~-1,~-5\right) $ . | 1 |
| 3874 | Find the angle between vectors $ \left(0,~2,~-1\right)$ and $\left(2,~1,~2\right)$. | 1 |
| 3875 | Find the magnitude of the vector $ \| \vec{v} \| = \left(5,~2\right) $ . | 1 |
| 3876 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-18,~-46\right) $ . | 1 |
| 3877 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-6 \sqrt{ 14 },~5\right) $ . | 1 |
| 3878 | Find the sum of the vectors $ \vec{v_1} = \left(-7,~-3\right) $ and $ \vec{v_2} = \left(-9,~-3\right) $ . | 1 |
| 3879 | Find the angle between vectors $ \left(-9,~12,~0\right)$ and $\left(0,~20,~0\right)$. | 1 |
| 3880 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-1,~4\right) $ . | 1 |
| 3881 | Find the angle between vectors $ \left(-4,~0\right)$ and $\left(-4,~4\right)$. | 1 |
| 3882 | Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~-2,~2\right) $ and $ \vec{v_2} = \left(0,~3,~3\right) $ . | 1 |
| 3883 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-3,~-2,~-1\right) $ . | 1 |
| 3884 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-5,~-3,~-6\right) $ . | 1 |
| 3885 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-5,~-3,~-6\right) $ and $ \vec{v_2} = \left(-3,~-2,~-1\right) $ . | 1 |
| 3886 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-1,~1,~-2\right) $ . | 1 |
| 3887 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-2,~-2 \sqrt{ 3 }\right) $ and $ \vec{v_2} = \left(-4 \sqrt{ 2 },~4 \sqrt{ 2 }\right) $ . | 1 |
| 3888 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~-2,~-1\right) $ and $ \vec{v_2} = \left(3,~-4,~-3\right) $ . | 1 |
| 3889 | Determine whether the vectors $ \vec{v_1} = \left(0,~0,~0\right) $, $ \vec{v_2} = \left(1,~2,~0\right) $ and $ \vec{v_3} = \left(1,~1,~1\right)$ are linearly independent or dependent. | 1 |
| 3890 | Find the difference of the vectors $ \vec{v_1} = \left(5,~0,~4\right) $ and $ \vec{v_2} = \left(1,~3,~-5\right) $ . | 1 |
| 3891 | Find the projection of the vector $ \vec{v_1} = \left(1,~-1,~1\right) $ on the vector $ \vec{v_2} = \left(1,~2,~2\right) $. | 1 |
| 3892 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-2,~5\right) $ and $ \vec{v_2} = \left(3,~7\right) $ . | 1 |
| 3893 | Find the projection of the vector $ \vec{v_1} = \left(-8,~-3\right) $ on the vector $ \vec{v_2} = \left(-12,~-7\right) $. | 1 |
| 3894 | Find the magnitude of the vector $ \| \vec{v} \| = \left(3,~-6\right) $ . | 1 |
| 3895 | Find the sum of the vectors $ \vec{v_1} = \left(0,~-\dfrac{ 981 }{ 4 }\right) $ and $ \vec{v_2} = \left(\dfrac{ 1691 }{ 50 },~\dfrac{ 1017 }{ 100 }\right) $ . | 1 |
| 3896 | Calculate the dot product of the vectors $ \vec{v_1} = \left(6,~2\right) $ and $ \vec{v_2} = \left(1,~5\right) $ . | 1 |
| 3897 | Find the angle between vectors $ \left(6,~-2,~-1\right)$ and $\left(3,~5,~3\right)$. | 1 |
| 3898 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~1,~1\right) $ and $ \vec{v_2} = \left(0,~1,~1\right) $ . | 1 |
| 3899 | Calculate the cross product of the vectors $ \vec{v_1} = \left(2,~-1,~0\right) $ and $ \vec{v_2} = \left(-1,~2,~0\right) $ . | 1 |
| 3900 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~2,~0\right) $ and $ \vec{v_2} = \left(-2,~1,~0\right) $ . | 1 |
