Vectors
(the database of solved problems)
All the problems and solutions shown below were generated using the Vectors Calculator.
| ID |
Problem |
Count |
| 3951 | Calculate the cross product of the vectors $ \vec{v_1} = \left(6,~-5,~-3\right) $ and $ \vec{v_2} = \left(4,~2,~2\right) $ . | 1 |
| 3952 | Find the magnitude of the vector $ \| \vec{v} \| = \left(6,~-5,~-3\right) $ . | 1 |
| 3953 | Calculate the cross product of the vectors $ \vec{v_1} = \left(5,~1,~8\right) $ and $ \vec{v_2} = \left(-1,~3,~6\right) $ . | 1 |
| 3954 | Find the magnitude of the vector $ \| \vec{v} \| = \left(2,~3,~-5\right) $ . | 1 |
| 3955 | Find the sum of the vectors $ \vec{v_1} = \left(2,~3,~-5\right) $ and $ \vec{v_2} = \left(4,~-2,~2\right) $ . | 1 |
| 3956 | Find the projection of the vector $ \vec{v_1} = \left(2,~3,~-5\right) $ on the vector $ \vec{v_2} = \left(4,~-2,~2\right) $. | 1 |
| 3957 | Find the magnitude of the vector $ \| \vec{v} \| = \left(3,~0,~3\right) $ . | 1 |
| 3958 | Find the difference of the vectors $ \vec{v_1} = \left(7,~-3\right) $ and $ \vec{v_2} = \left(-9,~6\right) $ . | 1 |
| 3959 | Find the angle between vectors $ \left(38,~-5,~7\right)$ and $\left(38,~4,~27\right)$. | 1 |
| 3960 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-3,~2,~-2\right) $ and $ \vec{v_2} = \left(3,~-2,~-4\right) $ . | 1 |
| 3961 | Find the sum of the vectors $ \vec{v_1} = \left(-4,~7\right) $ and $ \vec{v_2} = \left(5,~2\right) $ . | 1 |
| 3962 | Determine whether the vectors $ \vec{v_1} = \left(1,~2,~4\right) $, $ \vec{v_2} = \left(-\dfrac{ 1 }{ 2 },~-1,~-2\right) $ and $ \vec{v_3} = \left(0,~0,~0\right)$ are linearly independent or dependent. | 1 |
| 3963 | Find the angle between vectors $ \left(5,~2\right)$ and $\left(-6,~-1\right)$. | 1 |
| 3964 | Find the sum of the vectors $ \vec{v_1} = \left(36.2523,~16.9047\right) $ and $ \vec{v_2} = \left(0,~-75\right) $ . | 1 |
| 3965 | Find the sum of the vectors $ \vec{v_1} = \left(\dfrac{ 362523 }{ 10000 },~-\dfrac{ 580953 }{ 10000 }\right) $ and $ \vec{v_2} = \left(-22.9813,~-19.2836\right) $ . | 1 |
| 3966 | Find the sum of the vectors $ \vec{v_1} = \left(-5.3623,~-4.4995\right) $ and $ \vec{v_2} = \left(10.9274,~13.0228\right) $ . | 1 |
| 3967 | Find the magnitude of the vector $ \| \vec{v} \| = \left(63.6396,~63.6396\right) $ . | 1 |
| 3968 | Calculate the dot product of the vectors $ \vec{v_1} = \left(4,~-2\right) $ and $ \vec{v_2} = \left(6,~2\right) $ . | 1 |
| 3969 | Find the sum of the vectors $ \vec{v_1} = \left(3,~0\right) $ and $ \vec{v_2} = \left(1,~0\right) $ . | 1 |
| 3970 | Find the difference of the vectors $ \vec{v_1} = \left(3,~0\right) $ and $ \vec{v_2} = \left(1,~0\right) $ . | 1 |
| 3971 | Calculate the cross product of the vectors $ \vec{v_1} = \left(0,~3,~-6\right) $ and $ \vec{v_2} = \left(1,~2,~1\right) $ . | 1 |
| 3972 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-8,~6\right) $ . | 1 |
| 3973 | Find the angle between vectors $ \left(-8,~6\right)$ and $\left(2,~-9\right)$. | 1 |
| 3974 | Find the magnitude of the vector $ \| \vec{v} \| = \left(10,~15\right) $ . | 1 |
| 3975 | Find the projection of the vector $ \vec{v_1} = \left(3,~5\right) $ on the vector $ \vec{v_2} = \left(0,~8\right) $. | 1 |
| 3976 | Find the magnitude of the vector $ \| \vec{v} \| = \left(37.8,~39.6\right) $ . | 1 |
| 3977 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-8,~-5\right) $ and $ \vec{v_2} = \left(-10,~-6\right) $ . | 1 |
| 3978 | Find the angle between vectors $ \left(385,~167\right)$ and $\left(31,~187\right)$. | 1 |
| 3979 | Find the magnitude of the vector $ \| \vec{v} \| = \left(4,~-3,~0\right) $ . | 1 |
| 3980 | Find the magnitude of the vector $ \| \vec{v} \| = \left(3,~0,~4\right) $ . | 1 |
| 3981 | Calculate the dot product of the vectors $ \vec{v_1} = \left(4,~-3,~0\right) $ and $ \vec{v_2} = \left(3,~0,~4\right) $ . | 1 |
| 3982 | Calculate the cross product of the vectors $ \vec{v_1} = \left(4,~-3,~0\right) $ and $ \vec{v_2} = \left(3,~0,~4\right) $ . | 1 |
| 3983 | Find the magnitude of the vector $ \| \vec{v} \| = \left(1,~-2,~2\right) $ . | 1 |
| 3984 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-2,~2,~1\right) $ . | 1 |
| 3985 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~-2,~2\right) $ and $ \vec{v_2} = \left(-2,~2,~1\right) $ . | 1 |
| 3986 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~-2,~2\right) $ and $ \vec{v_2} = \left(-2,~2,~1\right) $ . | 1 |
| 3987 | Find the sum of the vectors $ \vec{v_1} = \left(3,~2\right) $ and $ \vec{v_2} = \left(8,~-4\right) $ . | 1 |
| 3988 | Find the magnitude of the vector $ \| \vec{v} \| = \left(22,~18\right) $ . | 1 |
| 3989 | Calculate the dot product of the vectors $ \vec{v_1} = \left(6,~7\right) $ and $ \vec{v_2} = \left(1,~8\right) $ . | 1 |
| 3990 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~4,~-5\right) $ and $ \vec{v_2} = \left(-0.9701,~0.2425,~0\right) $ . | 1 |
| 3991 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~4,~-5\right) $ and $ \vec{v_2} = \left(0,~0,~0\right) $ . | 1 |
| 3992 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~4,~-5\right) $ and $ \vec{v_2} = \left(0,~0,~0\right) $ . | 1 |
| 3993 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-2,~5\right) $ . | 1 |
| 3994 | Calculate the cross product of the vectors $ \vec{v_1} = \left(2,~-1,~2\right) $ and $ \vec{v_2} = \left(-1,~-2,~3\right) $ . | 1 |
| 3995 | Find the magnitude of the vector $ \| \vec{v} \| = \left(\dfrac{ 27 }{ 5 },~\dfrac{ 83 }{ 10 },~-\dfrac{ 47 }{ 5 }\right) $ . | 1 |
| 3996 | Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~-1,~1\right) $ and $ \vec{v_2} = \left(4,~2,~-2\right) $ . | 1 |
| 3997 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-11,~18,~-11\right) $ and $ \vec{v_2} = \left(-9,~-10,~19\right) $ . | 1 |
| 3998 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-11,~18,~-11\right) $ and $ \vec{v_2} = \left(-9,~-10,~19\right) $ . | 1 |
| 3999 | Find the sum of the vectors $ \vec{v_1} = \left(4,~-7\right) $ and $ \vec{v_2} = \left(2,~3\right) $ . | 1 |
| 4000 | Find the difference of the vectors $ \vec{v_1} = \left(3,~1\right) $ and $ \vec{v_2} = \left(-1,~4\right) $ . | 1 |
