Vectors
(the database of solved problems)
All the problems and solutions shown below were generated using the Vectors Calculator.
| ID |
Problem |
Count |
| 3751 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-4,~8,~10\right) $ and $ \vec{v_2} = \left(4,~2,~-6\right) $ . | 1 |
| 3752 | Find the magnitude of the vector $ \| \vec{v} \| = \left(5,~1,~-3\right) $ . | 1 |
| 3753 | Find the projection of the vector $ \vec{v_1} = \left(5,~1,~-3\right) $ on the vector $ \vec{v_2} = \left(4,~2,~-6\right) $. | 1 |
| 3754 | Determine whether the vectors $ \vec{v_1} = \left(2,~5,~7\right) $, $ \vec{v_2} = \left(4,~-1,~3\right) $ and $ \vec{v_3} = \left(10,~8,~-9\right)$ are linearly independent or dependent. | 1 |
| 3755 | Calculate the cross product of the vectors $ \vec{v_1} = \left(2,~5,~-8\right) $ and $ \vec{v_2} = \left(7,~-2,~3\right) $ . | 1 |
| 3756 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-1,~-62,~-39\right) $ and $ \vec{v_2} = \left(8,~2,~-1\right) $ . | 1 |
| 3757 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~-5,~9\right) $ and $ \vec{v_2} = \left(3,~4,~-7\right) $ . | 1 |
| 3758 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-1,~34,~19\right) $ and $ \vec{v_2} = \left(1,~0,~2\right) $ . | 1 |
| 3759 | Calculate the cross product of the vectors $ \vec{v_1} = \left(3,~4,~-7\right) $ and $ \vec{v_2} = \left(1,~0,~2\right) $ . | 1 |
| 3760 | Calculate the dot product of the vectors $ \vec{v_1} = \left(8,~-13,~-4\right) $ and $ \vec{v_2} = \left(1,~-5,~9\right) $ . | 1 |
| 3761 | Find the magnitude of the vector $ \| \vec{v} \| = \left(13,~4,~-16\right) $ . | 1 |
| 3762 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-7,~-1,~2\right) $ and $ \vec{v_2} = \left(-1,~1,~5\right) $ . | 1 |
| 3763 | Find the angle between vectors $ \left(0,~-5,~7\right)$ and $\left(-5,~1,~5\right)$. | 1 |
| 3764 | Find the magnitude of the vector $ \| \vec{v} \| = \left(0,~-5,~7\right) $ . | 1 |
| 3765 | Find the magnitude of the vector $ \| \vec{v} \| = \left(0,~-5,~7\right) $ . | 1 |
| 3766 | Find the magnitude of the vector $ \| \vec{v} \| = \left(2,~3,~-4\right) $ . | 1 |
| 3767 | Find the magnitude of the vector $ \| \vec{v} \| = \left(2,~-3,~1\right) $ . | 1 |
| 3768 | Calculate the cross product of the vectors $ \vec{v_1} = \left(2,~-3,~1\right) $ and $ \vec{v_2} = \left(-1,~1,~0\right) $ . | 1 |
| 3769 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-2,~3,~-4\right) $ and $ \vec{v_2} = \left(1,~1,~-7\right) $ . | 1 |
| 3770 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-2,~2\right) $ and $ \vec{v_2} = \left(8,~-8\right) $ . | 1 |
| 3771 | Calculate the cross product of the vectors $ \vec{v_1} = \left(3,~-5,~0\right) $ and $ \vec{v_2} = \left(-4,~-2,~0\right) $ . | 1 |
| 3772 | Find the magnitude of the vector $ \| \vec{v} \| = \left(4,~-1,~8\right) $ . | 1 |
| 3773 | Calculate the cross product of the vectors $ \vec{v_1} = \left(4,~-1,~8\right) $ and $ \vec{v_2} = \left(3,~1,~-1\right) $ . | 1 |
| 3774 | Find the angle between vectors $ \left(4,~-2,~1\right)$ and $\left(3,~2,~1\right)$. | 1 |
| 3775 | Find the magnitude of the vector $ \| \vec{v} \| = \left(12,~-12\right) $ . | 1 |
| 3776 | Find the difference of the vectors $ \vec{v_1} = \left(-6,~3,~3\right) $ and $ \vec{v_2} = \left(2,~10,~0\right) $ . | 1 |
| 3777 | Calculate the cross product of the vectors $ \vec{v_1} = \left(2,~1,~0\right) $ and $ \vec{v_2} = \left(2,~-1,~1\right) $ . | 1 |
| 3778 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~-2,~-4\right) $ and $ \vec{v_2} = \left(0,~1,~1\right) $ . | 1 |
| 3779 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~0,~-1\right) $ and $ \vec{v_2} = \left(6,~8,~6\right) $ . | 1 |
| 3780 | Calculate the cross product of the vectors $ \vec{v_1} = \left(4,~-20,~12\right) $ and $ \vec{v_2} = \left(2,~4,~6\right) $ . | 1 |
| 3781 | Find the magnitude of the vector $ \| \vec{v} \| = \left(4,~-5\right) $ . | 1 |
| 3782 | Find the difference of the vectors $ \vec{v_1} = \left(9,~-6,~21\right) $ and $ \vec{v_2} = \left(8,~6,~-4\right) $ . | 1 |
| 3783 | Find the sum of the vectors $ \vec{v_1} = \left(1,~2,~2\right) $ and $ \vec{v_2} = \left(3,~4,~12\right) $ . | 1 |
| 3784 | Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~-2,~7\right) $ and $ \vec{v_2} = \left(4,~3,~-2\right) $ . | 1 |
| 3785 | Find the sum of the vectors $ \vec{v_1} = \left(1,~2\right) $ and $ \vec{v_2} = \left(2,~5\right) $ . | 1 |
| 3786 | Find the angle between vectors $ \left(3,~-2,~7\right)$ and $\left(4,~3,~-2\right)$. | 1 |
| 3787 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~0,~-1\right) $ and $ \vec{v_2} = \left(\dfrac{ 4 }{ 5 },~0,~\dfrac{ 3 }{ 5 }\right) $ . | 1 |
| 3788 | Find the magnitude of the vector $ \| \vec{v} \| = \left(3,~-2,~7\right) $ . | 1 |
| 3789 | Find the magnitude of the vector $ \| \vec{v} \| = \left(12,~11\right) $ . | 1 |
| 3790 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-4,~5\right) $ . | 1 |
| 3791 | Find the sum of the vectors $ \vec{v_1} = \left(9,~4,~0\right) $ and $ \vec{v_2} = \left(1,~6,~7\right) $ . | 1 |
| 3792 | Find the sum of the vectors $ \vec{v_1} = \left(7,~1,~0\right) $ and $ \vec{v_2} = \left(1,~6,~7\right) $ . | 1 |
| 3793 | Calculate the dot product of the vectors $ \vec{v_1} = \left(7,~1,~0\right) $ and $ \vec{v_2} = \left(1,~6,~7\right) $ . | 1 |
| 3794 | Find the angle between vectors $ \left(7,~1,~0\right)$ and $\left(1,~6,~7\right)$. | 1 |
| 3795 | Find the sum of the vectors $ \vec{v_1} = \left(1,~4\right) $ and $ \vec{v_2} = \left(2,~-3\right) $ . | 1 |
| 3796 | Find the difference of the vectors $ \vec{v_1} = \left(-5,~2\right) $ and $ \vec{v_2} = \left(2,~-3\right) $ . | 1 |
| 3797 | Find the magnitude of the vector $ \| \vec{v} \| = \left(5,~1\right) $ . | 1 |
| 3798 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-\dfrac{ 1 }{ 2 },~\dfrac{ 3 }{ 2 },~-\dfrac{ 1 }{ 2 }\right) $ and $ \vec{v_2} = \left(0,~0,~0\right) $ . | 1 |
| 3799 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-3,~7,~2\right) $ and $ \vec{v_2} = \left(4,~3,~-5\right) $ . | 1 |
| 3800 | Calculate the dot product of the vectors $ \vec{v_1} = \left(0,~5,~3\right) $ and $ \vec{v_2} = \left(1,~7,~6\right) $ . | 1 |
