Vectors – Solved Problems Database
All the problems and solutions shown below were generated using the Vectors Calculator.
ID |
Problem |
Count |
5851 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-4,~-1,~0\right) $ and $ \vec{v_2} = \left(1,~3,~-2\right) $ . | 1 |
5852 | Find the sum of the vectors $ \vec{v_1} = \left(1,~-1\right) $ and $ \vec{v_2} = \left(-8,~6\right) $ . | 1 |
5853 | Find the angle between vectors $ \left(\dfrac{\sqrt{ 3 }}{ 2 },~0.5\right)$ and $\left(- \dfrac{\sqrt{ 2 }}{ 2 },~- \dfrac{\sqrt{ 2 }}{ 2 }\right)$. | 1 |
5854 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-7,~-6\right) $ . | 1 |
5855 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~1\right) $ and $ \vec{v_2} = \left(2,~5\right) $ . | 1 |
5856 | Find the angle between vectors $ \left(3,~2,~2\right)$ and $\left(-1,~-4,~1\right)$. | 1 |
5857 | Find the magnitude of the vector $ \| \vec{v} \| = \left(2,~7,~5\right) $ . | 1 |
5858 | Calculate the cross product of the vectors $ \vec{v_1} = \left(6,~-5,~1\right) $ and $ \vec{v_2} = \left(2,~1,~-4\right) $ . | 1 |
5859 | Find the sum of the vectors $ \vec{v_1} = \left(-5,~7\right) $ and $ \vec{v_2} = \left(-7,~4\right) $ . | 1 |
5860 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~4,~-4\right) $ and $ \vec{v_2} = \left(0,~3,~2\right) $ . | 1 |
5861 | Calculate the cross product of the vectors $ \vec{v_1} = \left(4,~-2,~1\right) $ and $ \vec{v_2} = \left(3,~-4,~1\right) $ . | 1 |
5862 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~1,~1\right) $ and $ \vec{v_2} = \left(0,~2,~2\right) $ . | 1 |
5863 | Find the angle between vectors $ \left(\sqrt{ 3 },~-1\right)$ and $\left(0,~7\right)$. | 1 |
5864 | Calculate the cross product of the vectors $ \vec{v_1} = \left(4,~-4,~3\right) $ and $ \vec{v_2} = \left(3,~-1,~-3\right) $ . | 1 |
5865 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-2,~5\right) $ . | 1 |
5866 | 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 |
5867 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1000,~0\right) $ and $ \vec{v_2} = \left(530,~15\right) $ . | 1 |
5868 | Find the difference of the vectors $ \vec{v_1} = \left(\dfrac{ 259 }{ 100 },~\dfrac{ 3 }{ 2 }\right) $ and $ \vec{v_2} = \left(0,~3\right) $ . | 1 |
5869 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-3,~9\right) $ . | 1 |
5870 | Find the sum of the vectors $ \vec{v_1} = \left(-1,~-1\right) $ and $ \vec{v_2} = \left(-1,~\dfrac{ 3 }{ 2 }\right) $ . | 1 |
5871 | Find the sum of the vectors $ \vec{v_1} = \left(3,~2\right) $ and $ \vec{v_2} = \left(7,~2\right) $ . | 1 |
5872 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-4 \sqrt{ 3 },~4\right) $ . | 1 |
5873 | Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~2,~1\right) $ and $ \vec{v_2} = \left(2,~-5,~3\right) $ . | 1 |
5874 | Determine whether the vectors $ \vec{v_1} = \left(1,~2\right) $ and $ \vec{v_2} = \left(2,~4\right) $ are linearly independent or dependent. | 1 |
5875 | Find the difference of the vectors $ \vec{v_1} = \left(-2,~1,~4\right) $ and $ \vec{v_2} = \left(4,~-3,~5\right) $ . | 1 |
5876 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~7,~1\right) $ and $ \vec{v_2} = \left(1,~10,~1\right) $ . | 1 |
5877 | Find the magnitude of the vector $ \| \vec{v} \| = \left(4,~2,~2\right) $ . | 1 |
5878 | Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~2,~2\right) $ and $ \vec{v_2} = \left(-10,~5,~10\right) $ . | 1 |
5879 | Find the magnitude of the vector $ \| \vec{v} \| = \left(0,~0,~0\right) $ . | 1 |
5880 | Find the sum of the vectors $ \vec{v_1} = \left(-5,~7\right) $ and $ \vec{v_2} = \left(3,~-10\right) $ . | 1 |
5881 | Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~4,~12\right) $ and $ \vec{v_2} = \left(2,~-2,~4\right) $ . | 1 |
5882 | Find the angle between vectors $ \left(1,~2,~-1\right)$ and $\left(2,~1,~1\right)$. | 1 |
5883 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-4,~8,~10\right) $ and $ \vec{v_2} = \left(5,~1,~-3\right) $ . | 1 |
5884 | 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 |
5885 | Find the projection of the vector $ \vec{v_1} = \left(4,~-4\right) $ on the vector $ \vec{v_2} = \left(3,~2\right) $. | 1 |
5886 | Find the magnitude of the vector $ \| \vec{v} \| = \left(40,~21,~60\right) $ . | 1 |
5887 | Find the angle between vectors $ \left(2,~-\dfrac{ 3999 }{ 1000 }\right)$ and $\left(4,~2\right)$. | 1 |
5888 | Find the sum of the vectors $ \vec{v_1} = \left(2,~4,~7\right) $ and $ \vec{v_2} = \left(0,~3,~-4\right) $ . | 1 |
5889 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-1,~-4,~2\right) $ and $ \vec{v_2} = \left(2,~2,~1\right) $ . | 1 |
5890 | Find the sum of the vectors $ \vec{v_1} = \left(3,~12\right) $ and $ \vec{v_2} = \left(0,~6\right) $ . | 1 |
5891 | Find the sum of the vectors $ \vec{v_1} = \left(-2,~2\right) $ and $ \vec{v_2} = \left(-3,~-3\right) $ . | 1 |
5892 | Find the magnitude of the vector $ \| \vec{v} \| = \left(5,~0\right) $ . | 1 |
5893 | Find the projection of the vector $ \vec{v_1} = \left(4,~5\right) $ on the vector $ \vec{v_2} = \left(6,~8\right) $. | 1 |
5894 | Calculate the dot product of the vectors $ \vec{v_1} = \left(4,~9\right) $ and $ \vec{v_2} = \left(2,~-1\right) $ . | 1 |
5895 | Find the difference of the vectors $ \vec{v_1} = \left(4,~2,~6\right) $ and $ \vec{v_2} = \left(6,~3,~2\right) $ . | 1 |
5896 | Calculate the dot product of the vectors $ \vec{v_1} = \left(7,~1\right) $ and $ \vec{v_2} = \left(1,~7\right) $ . | 1 |
5897 | Find the magnitude of the vector $ \| \vec{v} \| = \left(2,~1,~3\right) $ . | 1 |
5898 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~-1,~-2\right) $ and $ \vec{v_2} = \left(1,~0,~0\right) $ . | 1 |
5899 | Find the projection of the vector $ \vec{v_1} = \left(1,~1,~1\right) $ on the vector $ \vec{v_2} = \left(3,~4,~5\right) $. | 1 |
5900 | Find the magnitude of the vector $ \| \vec{v} \| = \left(43,~30\right) $ . | 1 |