Vectors
(the database of solved problems)
All the problems and solutions shown below were generated using the Vectors Calculator.
| ID |
Problem |
Count |
| 3901 | Find the sum of the vectors $ \vec{v_1} = \left(1,~2,~0\right) $ and $ \vec{v_2} = \left(-2,~1,~0\right) $ . | 1 |
| 3902 | Find the sum of the vectors $ \vec{v_1} = \left(2,~-7,~3\right) $ and $ \vec{v_2} = \left(-1,~5,~8\right) $ . | 1 |
| 3903 | Calculate the cross product of the vectors $ \vec{v_1} = \left(2,~-7,~3\right) $ and $ \vec{v_2} = \left(-1,~5,~8\right) $ . | 1 |
| 3904 | Find the difference of the vectors $ \vec{v_1} = \left(-1,~5,~8\right) $ and $ \vec{v_2} = \left(2,~-7,~3\right) $ . | 1 |
| 3905 | Find the difference of the vectors $ \vec{v_1} = \left(-2,~1,~0\right) $ and $ \vec{v_2} = \left(1,~2,~0\right) $ . | 1 |
| 3906 | Find the difference of the vectors $ \vec{v_1} = \left(0,~0,~0\right) $ and $ \vec{v_2} = \left(1,~2,~0\right) $ . | 1 |
| 3907 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-3,~-1,~0\right) $ and $ \vec{v_2} = \left(-1,~-2,~0\right) $ . | 1 |
| 3908 | Calculate the cross product of the vectors $ \vec{v_1} = \left(0,~3,~0\right) $ and $ \vec{v_2} = \left(0,~0,~1\right) $ . | 1 |
| 3909 | Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~0,~1\right) $ and $ \vec{v_2} = \left(3,~0,~0\right) $ . | 1 |
| 3910 | 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 |
| 3911 | Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~0,~0\right) $ and $ \vec{v_2} = \left(0,~-2,~2\right) $ . | 1 |
| 3912 | Find the projection of the vector $ \vec{v_1} = \left(-6,~0,~5\right) $ on the vector $ \vec{v_2} = \left(1,~3,~-3\right) $. | 1 |
| 3913 | Find the difference of the vectors $ \vec{v_1} = \left(-109914,~75574,~4614\right) $ and $ \vec{v_2} = \left(-118365,~77821,~5275\right) $ . | 1 |
| 3914 | Find the magnitude of the vector $ \| \vec{v} \| = \left(8451,~-2247,~-661\right) $ . | 1 |
| 3915 | Calculate the cross product of the vectors $ \vec{v_1} = \left(2,~4,~0\right) $ and $ \vec{v_2} = \left(0,~3,~-5\right) $ . | 1 |
| 3916 | Find the difference of the vectors $ \vec{v_1} = \left(-107253,~83672,~4181\right) $ and $ \vec{v_2} = \left(-112571,~84706,~4980\right) $ . | 1 |
| 3917 | Find the magnitude of the vector $ \| \vec{v} \| = \left(5318,~-1034,~-799\right) $ . | 1 |
| 3918 | Calculate the cross product of the vectors $ \vec{v_1} = \left(0,~3,~-5\right) $ and $ \vec{v_2} = \left(2,~4,~0\right) $ . | 1 |
| 3919 | Calculate the cross product of the vectors $ \vec{v_1} = \left(2,~-3,~1\right) $ and $ \vec{v_2} = \left(4,~-4,~1\right) $ . | 1 |
| 3920 | Calculate the cross product of the vectors $ \vec{v_1} = \left(0,~1,~2\right) $ and $ \vec{v_2} = \left(-3,~4,~0\right) $ . | 1 |
| 3921 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~0,~2\right) $ and $ \vec{v_2} = \left(0,~3,~3\right) $ . | 1 |
| 3922 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~2,~0\right) $ and $ \vec{v_2} = \left(0,~1,~1\right) $ . | 1 |
| 3923 | 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 |
| 3924 | Calculate the cross product of the vectors $ \vec{v_1} = \left(2,~0,~2\right) $ and $ \vec{v_2} = \left(0,~2,~2\right) $ . | 1 |
| 3925 | Find the sum of the vectors $ \vec{v_1} = \left(\dfrac{ 13 }{ 10 },~140\right) $ and $ \vec{v_2} = \left(\dfrac{ 6 }{ 5 },~50\right) $ . | 1 |
| 3926 | Find the difference of the vectors $ \vec{v_1} = \left(2,~4\right) $ and $ \vec{v_2} = \left(-3,~-4\right) $ . | 1 |
| 3927 | Find the angle between vectors $ \left(1,~2,~4\right)$ and $\left(3,~-2,~1\right)$. | 1 |
| 3928 | Find the sum of the vectors $ \vec{v_1} = \left(16,~0\right) $ and $ \vec{v_2} = \left(0,~1\right) $ . | 1 |
| 3929 | Find the difference of the vectors $ \vec{v_1} = \left(1,~0,~10\right) $ and $ \vec{v_2} = \left(5,~-5,~3\right) $ . | 1 |
| 3930 | Find the sum of the vectors $ \vec{v_1} = \left(2,~1,~-1\right) $ and $ \vec{v_2} = \left(-1,~-2,~5\right) $ . | 1 |
| 3931 | Determine whether the vectors $ \vec{v_1} = \left(2,~1,~-1\right) $, $ \vec{v_2} = \left(-1,~-2,~5\right) $ and $ \vec{v_3} = \left(0,~0,~0\right)$ are linearly independent or dependent. | 1 |
| 3932 | Calculate the cross product of the vectors $ \vec{v_1} = \left(2,~1,~-1\right) $ and $ \vec{v_2} = \left(-1,~-2,~5\right) $ . | 1 |
| 3933 | 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 |
| 3934 | Find the magnitude of the vector $ \| \vec{v} \| = \left(4,~5,~-2\right) $ . | 1 |
| 3935 | Find the angle between vectors $ \left(1,~3,~-1\right)$ and $\left(-3,~-9,~3\right)$. | 1 |
| 3936 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-3,~-9,~3\right) $ . | 1 |
| 3937 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~3,~-1\right) $ and $ \vec{v_2} = \left(-3,~-9,~3\right) $ . | 1 |
| 3938 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-1,~-2,~5\right) $ and $ \vec{v_2} = \left(2,~1,~-3\right) $ . | 1 |
| 3939 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~2,~5\right) $ and $ \vec{v_2} = \left(2,~-5,~0\right) $ . | 1 |
| 3940 | Calculate the cross product of the vectors $ \vec{v_1} = \left(3,~-3,~5\right) $ and $ \vec{v_2} = \left(-1,~7,~5\right) $ . | 1 |
| 3941 | Find the magnitude of the vector $ \| \vec{v} \| = \left(2,~1,~-3\right) $ . | 1 |
| 3942 | Find the magnitude of the vector $ \| \vec{v} \| = \left(3,~0,~-1\right) $ . | 1 |
| 3943 | Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~1,~-2\right) $ and $ \vec{v_2} = \left(-2,~3,~6\right) $ . | 1 |
| 3944 | Find the angle between vectors $ \left(5,~-5,~-4\right)$ and $\left(3,~-4,~-1\right)$. | 1 |
| 3945 | Find the difference of the vectors $ \vec{v_1} = \left(0,~-5\right) $ and $ \vec{v_2} = \left(-6,~-8\right) $ . | 1 |
| 3946 | Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~-5,~5\right) $ and $ \vec{v_2} = \left(4,~-5,~-3\right) $ . | 1 |
| 3947 | Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~-5,~5\right) $ and $ \vec{v_2} = \left(2,~-5,~5\right) $ . | 1 |
| 3948 | Find the sum of the vectors $ \vec{v_1} = \left(-7,~-6\right) $ and $ \vec{v_2} = \left(0,~1\right) $ . | 1 |
| 3949 | Find the sum of the vectors $ \vec{v_1} = \left(1,~-8,~-9\right) $ and $ \vec{v_2} = \left(0,~0,~0\right) $ . | 1 |
| 3950 | Calculate the dot product of the vectors $ \vec{v_1} = \left(6,~-5,~-3\right) $ and $ \vec{v_2} = \left(4,~2,~2\right) $ . | 1 |
