Vectors
(the database of solved problems)
All the problems and solutions shown below were generated using the Vectors Calculator.
| ID |
Problem |
Count |
| 5951 | Find the sum of the vectors $ \vec{v_1} = \left(-5,~4,~-2\right) $ and $ \vec{v_2} = \left(3,~4,~-1\right) $ . | 1 |
| 5952 | Find the angle between vectors $ \left(-5,~4,~-2\right)$ and $\left(3,~4,~-1\right)$. | 1 |
| 5953 | Find the angle between vectors $ \left(9,~-6,~3\right)$ and $\left(-6,~4,~-2\right)$. | 1 |
| 5954 | Find the sum of the vectors $ \vec{v_1} = \left(1,~-6\right) $ and $ \vec{v_2} = \left(-15,~8\right) $ . | 1 |
| 5955 | Find the projection of the vector $ \vec{v_1} = \left(1,~-6\right) $ on the vector $ \vec{v_2} = \left(-15,~8\right) $. | 1 |
| 5956 | Find the difference of the vectors $ \vec{v_1} = \left(4,~9\right) $ and $ \vec{v_2} = \left(3,~-9\right) $ . | 1 |
| 5957 | Find the sum of the vectors $ \vec{v_1} = \left(3,~1\right) $ and $ \vec{v_2} = \left(2,~2\right) $ . | 1 |
| 5958 | Calculate the cross product of the vectors $ \vec{v_1} = \left(4,~5,~0\right) $ and $ \vec{v_2} = \left(-9,~1,~3\right) $ . | 1 |
| 5959 | Find the difference of the vectors $ \vec{v_1} = \left(5,~4\right) $ and $ \vec{v_2} = \left(5,~6\right) $ . | 1 |
| 5960 | Find the angle between vectors $ \left(-4,~5\right)$ and $\left(0,~3\right)$. | 1 |
| 5961 | Calculate the cross product of the vectors $ \vec{v_1} = \left(3,~-2,~5\right) $ and $ \vec{v_2} = \left(2,~1,~4\right) $ . | 1 |
| 5962 | Calculate the dot product of the vectors $ \vec{v_1} = \left(5,~3,~0\right) $ and $ \vec{v_2} = \left(1,~0,~5\right) $ . | 1 |
| 5963 | Find the sum of the vectors $ \vec{v_1} = \left(6,~9,~-1\right) $ and $ \vec{v_2} = \left(6,~-7,~0\right) $ . | 1 |
| 5964 | Find the sum of the vectors $ \vec{v_1} = \left(-1,~2,~-5\right) $ and $ \vec{v_2} = \left(1,~4,~-3\right) $ . | 1 |
| 5965 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~6,~-8\right) $ and $ \vec{v_2} = \left(4,~-2,~-1\right) $ . | 1 |
| 5966 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~2,~-4\right) $ and $ \vec{v_2} = \left(-5,~3,~-7\right) $ . | 1 |
| 5967 | Find the magnitude of the vector $ \| \vec{v} \| = \left(6,~0,~8\right) $ . | 1 |
| 5968 | Find the angle between vectors $ \left(2,~1,~-3\right)$ and $\left(4,~-2,~6\right)$. | 1 |
| 5969 | Find the magnitude of the vector $ \| \vec{v} \| = \left(2,~3,~4\right) $ . | 1 |
| 5970 | Find the magnitude of the vector $ \| \vec{v} \| = \left(5,~-2,~1\right) $ . | 1 |
| 5971 | Calculate the cross product of the vectors $ \vec{v_1} = \left(5,~-2,~1\right) $ and $ \vec{v_2} = \left(1,~0,~3\right) $ . | 1 |
| 5972 | Find the magnitude of the vector $ \| \vec{v} \| = \left(1,~-3\right) $ . | 1 |
| 5973 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~-3\right) $ and $ \vec{v_2} = \left(-2,~4\right) $ . | 1 |
| 5974 | Calculate the cross product of the vectors $ \vec{v_1} = \left(6,~-1,~2\right) $ and $ \vec{v_2} = \left(2,~3,~-4\right) $ . | 1 |
| 5975 | Calculate the dot product of the vectors $ \vec{v_1} = \left(4,~2,~-1\right) $ and $ \vec{v_2} = \left(-3,~0,~5\right) $ . | 1 |
| 5976 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~2,~3\right) $ and $ \vec{v_2} = \left(4,~-5,~6\right) $ . | 1 |
| 5977 | Calculate the cross product of the vectors $ \vec{v_1} = \left(0,~3,~-2\right) $ and $ \vec{v_2} = \left(4,~-1,~2\right) $ . | 1 |
| 5978 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~-1,~2\right) $ and $ \vec{v_2} = \left(3,~2,~-1\right) $ . | 1 |
| 5979 | Calculate the cross product of the vectors $ \vec{v_1} = \left(2,~4,~6\right) $ and $ \vec{v_2} = \left(-1,~0,~3\right) $ . | 1 |
| 5980 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-3,~5\right) $ and $ \vec{v_2} = \left(1,~-2\right) $ . | 1 |
| 5981 | Find the magnitude of the vector $ \| \vec{v} \| = \left(2,~2\right) $ . | 1 |
| 5982 | Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~-3\right) $ and $ \vec{v_2} = \left(-4,~0\right) $ . | 1 |
| 5983 | Find the sum of the vectors $ \vec{v_1} = \left(1,~-3,~1\right) $ and $ \vec{v_2} = \left(2,~7,~0\right) $ . | 1 |
| 5984 | Find the magnitude of the vector $ \| \vec{v} \| = \left(\dfrac{ 59 }{ 5 },~0\right) $ . | 1 |
| 5985 | Find the projection of the vector $ \vec{v_1} = \left(-2,~4,~1\right) $ on the vector $ \vec{v_2} = \left(2,~5,~1\right) $. | 1 |
| 5986 | Find the projection of the vector $ \vec{v_1} = \left(-2,~4,~1\right) $ on the vector $ \vec{v_2} = \left(2,~5,~-1\right) $. | 1 |
| 5987 | Find the angle between vectors $ \left(4,~-2,~6\right)$ and $\left(-2,~1,~-3\right)$. | 1 |
| 5988 | Calculate the cross product of the vectors $ \vec{v_1} = \left(2,~\sqrt{ 3 },~7\right) $ and $ \vec{v_2} = \left(-6,~4,~\sqrt{ 2 }\right) $ . | 1 |
| 5989 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-3,~1,~2\right) $ and $ \vec{v_2} = \left(-2,~3,~-1\right) $ . | 1 |
| 5990 | Calculate the cross product of the vectors $ \vec{v_1} = \left(\dfrac{ 2 }{ 5 },~\dfrac{ 3 }{ 5 },~\dfrac{ 1 }{ 5 }\right) $ and $ \vec{v_2} = \left(\dfrac{ 9 }{ 2 },~\dfrac{ 8 }{ 5 },~-\dfrac{ 7 }{ 5 }\right) $ . | 1 |
| 5991 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~-2,~1\right) $ and $ \vec{v_2} = \left(2,~1,~2\right) $ . | 1 |
| 5992 | Calculate the cross product of the vectors $ \vec{v_1} = \left(0,~-1,~0\right) $ and $ \vec{v_2} = \left(\dfrac{ 99 }{ 100 },~0,~0\right) $ . | 1 |
| 5993 | Find the sum of the vectors $ \vec{v_1} = \left(4,~-4,~4\right) $ and $ \vec{v_2} = \left(3,~-13,~10\right) $ . | 1 |
| 5994 | Find the angle between vectors $ \left(-1,~1,~13\right)$ and $\left(-1,~3,~3\right)$. | 1 |
| 5995 | Find the sum of the vectors $ \vec{v_1} = \left(-3,~1\right) $ and $ \vec{v_2} = \left(4,~5\right) $ . | 1 |
| 5996 | Find the sum of the vectors $ \vec{v_1} = \left(3,~11\right) $ and $ \vec{v_2} = \left(3,~-4\right) $ . | 1 |
| 5997 | Find the difference of the vectors $ \vec{v_1} = \left(1,~2\right) $ and $ \vec{v_2} = \left(-4,~12\right) $ . | 1 |
| 5998 | Find the difference of the vectors $ \vec{v_1} = \left(2,~2\right) $ and $ \vec{v_2} = \left(4,~7\right) $ . | 1 |
| 5999 | Find the sum of the vectors $ \vec{v_1} = \left(4,~2\right) $ and $ \vec{v_2} = \left(8,~-2\right) $ . | 1 |
| 6000 | Calculate the dot product of the vectors $ \vec{v_1} = \left(7,~5\right) $ and $ \vec{v_2} = \left(-9,~7\right) $ . | 1 |
