Vectors – Solved Problems Database
All the problems and solutions shown below were generated using the Vectors Calculator.
ID |
Problem |
Count |
5951 | Find the angle between vectors $ \left(5,~0\right)$ and $\left(-1,~5\right)$. | 1 |
5952 | Calculate the cross product of the vectors $ \vec{v_1} = \left(7,~1,~0\right) $ and $ \vec{v_2} = \left(2,~9,~0\right) $ . | 1 |
5953 | Calculate the cross product of the vectors $ \vec{v_1} = \left(2,~3,~7\right) $ and $ \vec{v_2} = \left(3,~-2,~-3\right) $ . | 1 |
5954 | Find the difference of the vectors $ \vec{v_1} = \left(4,~-5,~-3\right) $ and $ \vec{v_2} = \left(4,~-3,~5\right) $ . | 1 |
5955 | Calculate the cross product of the vectors $ \vec{v_1} = \left(3,~-1,~-4\right) $ and $ \vec{v_2} = \left(0,~0,~0\right) $ . | 1 |
5956 | Find the difference of the vectors $ \vec{v_1} = \left(24,~40\right) $ and $ \vec{v_2} = \left(-20,~29\right) $ . | 1 |
5957 | Find the sum of the vectors $ \vec{v_1} = \left(-3,~1\right) $ and $ \vec{v_2} = \left(4,~5\right) $ . | 1 |
5958 | Calculate the cross product of the vectors $ \vec{v_1} = \left(0,~4,~0\right) $ and $ \vec{v_2} = \left(\dfrac{ 353553 }{ 50000 },~\dfrac{ 353553 }{ 50000 },~0\right) $ . | 1 |
5959 | Find the difference of the vectors $ \vec{v_1} = \left(5,~6\right) $ and $ \vec{v_2} = \left(8,~1\right) $ . | 1 |
5960 | Find the magnitude of the vector $ \| \vec{v} \| = \left(5,~13\right) $ . | 1 |
5961 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~-1,~-2\right) $ and $ \vec{v_2} = \left(3,~-1,~-2\right) $ . | 1 |
5962 | Calculate the dot product of the vectors $ \vec{v_1} = \left(15,~-8\right) $ and $ \vec{v_2} = \left(-5,~12\right) $ . | 1 |
5963 | Calculate the cross product of the vectors $ \vec{v_1} = \left(\dfrac{ 3 }{ 10 },~-\dfrac{ 2 }{ 5 },~0\right) $ and $ \vec{v_2} = \left(0,~0,~\dfrac{ 1 }{ 10 }\right) $ . | 1 |
5964 | Find the sum of the vectors $ \vec{v_1} = \left(-1,~4\right) $ and $ \vec{v_2} = \left(3,~2\right) $ . | 1 |
5965 | Calculate the cross product of the vectors $ \vec{v_1} = \left(8,~-4,~-3\right) $ and $ \vec{v_2} = \left(2,~1,~-4\right) $ . | 1 |
5966 | Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~4\right) $ and $ \vec{v_2} = \left(3,~9\right) $ . | 1 |
5967 | Find the sum of the vectors $ \vec{v_1} = \left(4,~6\right) $ and $ \vec{v_2} = \left(5,~2\right) $ . | 1 |
5968 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-3,~2\right) $ . | 1 |
5969 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~2,~2\right) $ and $ \vec{v_2} = \left(-4,~7,~-6\right) $ . | 1 |
5970 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-9,~7,~5\right) $ and $ \vec{v_2} = \left(9,~3,~2\right) $ . | 1 |
5971 | Find the magnitude of the vector $ \| \vec{v} \| = \left(5,~1,~-3\right) $ . | 1 |
5972 | Find the angle between vectors $ \left(0,~2,~-1\right)$ and $\left(2,~1,~2\right)$. | 1 |
5973 | Find the projection of the vector $ \vec{v_1} = \left(-4,~8,~10\right) $ on the vector $ \vec{v_2} = \left(2,~-4,~5\right) $. | 1 |
5974 | Find the magnitude of the vector $ \| \vec{v} \| = \left(0.0211,~0.0066\right) $ . | 1 |
5975 | Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~-3,~5\right) $ and $ \vec{v_2} = \left(-2,~4,~-1\right) $ . | 1 |
5976 | Find the magnitude of the vector $ \| \vec{v} \| = \left(0,~10\right) $ . | 1 |
5977 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-12,~9\right) $ . | 1 |
5978 | Find the magnitude of the vector $ \| \vec{v} \| = \left(6,~-6\right) $ . | 1 |
5979 | Find the difference of the vectors $ \vec{v_1} = \left(-5,~-1\right) $ and $ \vec{v_2} = \left(-3,~-4\right) $ . | 1 |
5980 | Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~7,~5\right) $ and $ \vec{v_2} = \left(2,~9,~4\right) $ . | 1 |
5981 | Find the angle between vectors $ \left(15,~-8\right)$ and $\left(-5,~12\right)$. | 1 |
5982 | Find the difference of the vectors $ \vec{v_1} = \left(-1,~4\right) $ and $ \vec{v_2} = \left(3,~2\right) $ . | 1 |
5983 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~2,~-4\right) $ and $ \vec{v_2} = \left(0,~5,~2\right) $ . | 1 |
5984 | Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~-2,~-5\right) $ and $ \vec{v_2} = \left(20,~-2,~3\right) $ . | 1 |
5985 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-3,~-4\right) $ . | 1 |
5986 | Find the angle between vectors $ \left(-9,~7,~5\right)$ and $\left(9,~3,~2\right)$. | 1 |
5987 | Calculate the cross product of the vectors $ \vec{v_1} = \left(4,~2,~-4\right) $ and $ \vec{v_2} = \left(2,~7,~3\right) $ . | 1 |
5988 | Calculate the cross product of the vectors $ \vec{v_1} = \left(8,~-9,~10\right) $ and $ \vec{v_2} = \left(0,~1,~2\right) $ . | 1 |
5989 | Find the projection of the vector $ \vec{v_1} = \left(3,~3,~-2\right) $ on the vector $ \vec{v_2} = \left(2,~2,~-4\right) $. | 1 |
5990 | Find the sum of the vectors $ \vec{v_1} = \left(-2,~0,~-1\right) $ and $ \vec{v_2} = \left(0,~-1,~3\right) $ . | 1 |
5991 | Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~2,~0\right) $ and $ \vec{v_2} = \left(1,~7,~2\right) $ . | 1 |
5992 | Calculate the dot product of the vectors $ \vec{v_1} = \left(240,~300\right) $ and $ \vec{v_2} = \left(2.9,~3.08\right) $ . | 1 |
5993 | Find the angle between vectors $ \left(\dfrac{ 1 }{ 2 },~\dfrac{ 1 }{ 2 }\right)$ and $\left(-\dfrac{ 1 }{ 2 },~-\dfrac{ 1 }{ 2 }\right)$. | 1 |
5994 | Find the angle between vectors $ \left(-11,~0,~6\right)$ and $\left(1,~2,~3\right)$. | 1 |
5995 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~-4,~2\right) $ and $ \vec{v_2} = \left(4,~0,~-1\right) $ . | 1 |
5996 | Calculate the cross product of the vectors $ \vec{v_1} = \left(3,~7,~5\right) $ and $ \vec{v_2} = \left(2,~9,~4\right) $ . | 1 |
5997 | Find the difference of the vectors $ \vec{v_1} = \left(-1,~2\right) $ and $ \vec{v_2} = \left(3,~0\right) $ . | 1 |
5998 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-2,~\dfrac{ 2 }{ 3 },~-3\right) $ and $ \vec{v_2} = \left(4,~0,~-\dfrac{ 1 }{ 2 }\right) $ . | 1 |
5999 | Find the difference of the vectors $ \vec{v_1} = \left(0,~-16\right) $ and $ \vec{v_2} = \left(12,~-20\right) $ . | 1 |
6000 | Calculate the dot product of the vectors $ \vec{v_1} = \left(0,~4,~-2\right) $ and $ \vec{v_2} = \left(3,~-1,~-2\right) $ . | 1 |