Vectors – Solved Problems Database
All the problems and solutions shown below were generated using the Vectors Calculator.
ID |
Problem |
Count |
5751 | Calculate the cross product of the vectors $ \vec{v_1} = \left(5,~6,~-5\right) $ and $ \vec{v_2} = \left(8,~0,~-7\right) $ . | 1 |
5752 | Find the difference of the vectors $ \vec{v_1} = \left(84,~84\right) $ and $ \vec{v_2} = \left(53,~53\right) $ . | 1 |
5753 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-\dfrac{ 4 }{ 9 },~\dfrac{ 8 }{ 9 },~\dfrac{ 1 }{ 9 }\right) $ and $ \vec{v_2} = \left(-\dfrac{ 7 }{ 9 },~-\dfrac{ 4 }{ 9 },~\dfrac{ 4 }{ 9 }\right) $ . | 1 |
5754 | Find the angle between vectors $ \left(-11,~9\right)$ and $\left(-8,~-4\right)$. | 1 |
5755 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-1,~-10,~-2\right) $ and $ \vec{v_2} = \left(0,~0,~0\right) $ . | 1 |
5756 | Calculate the cross product of the vectors $ \vec{v_1} = \left(4,~8,~-6\right) $ and $ \vec{v_2} = \left(7,~4,~-1\right) $ . | 1 |
5757 | Find the difference of the vectors $ \vec{v_1} = \left(\dfrac{ 4427 }{ 5000 },~\dfrac{ 4427 }{ 2500 }\right) $ and $ \vec{v_2} = \left(-1,~-2\right) $ . | 1 |
5758 | Find the sum of the vectors $ \vec{v_1} = \left(3,~3\right) $ and $ \vec{v_2} = \left(-5,~-1\right) $ . | 1 |
5759 | Find the sum of the vectors $ \vec{v_1} = \left(-6,~9\right) $ and $ \vec{v_2} = \left(3,~-7\right) $ . | 1 |
5760 | Find the angle between vectors $ \left(1,~0,~2\right)$ and $\left(2,~-1,~1\right)$. | 1 |
5761 | Find the magnitude of the vector $ \| \vec{v} \| = \left(12,~11\right) $ . | 1 |
5762 | Find the angle between vectors $ \left(5,~-2,~0\right)$ and $\left(-3,~-3,~-2\right)$. | 1 |
5763 | Find the sum of the vectors $ \vec{v_1} = \left(3,~8\right) $ and $ \vec{v_2} = \left(-4,~-2\right) $ . | 1 |
5764 | Find the angle between vectors $ \left(1,~2,~3\right)$ and $\left(1,~1,~1\right)$. | 1 |
5765 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~1,~1\right) $ and $ \vec{v_2} = \left(3,~-5,~4\right) $ . | 1 |
5766 | Find the magnitude of the vector $ \| \vec{v} \| = \left(\dfrac{ 24 }{ 5 },~0,~0\right) $ . | 1 |
5767 | Determine whether the vectors $ \vec{v_1} = \left(6,~-3\right) $ and $ \vec{v_2} = \left(-2,~8\right) $ are linearly independent or dependent. | 1 |
5768 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-2,~3\right) $ . | 1 |
5769 | Find the angle between vectors $ \left(3,~-4\right)$ and $\left(5,~2\right)$. | 1 |
5770 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~8,~3\right) $ and $ \vec{v_2} = \left(-2,~9,~1\right) $ . | 1 |
5771 | Find the projection of the vector $ \vec{v_1} = \left(1,~1\right) $ on the vector $ \vec{v_2} = \left(2,~5\right) $. | 1 |
5772 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-\dfrac{ 185 }{ 26 },~0,~\dfrac{ 37 }{ 26 }\right) $ . | 1 |
5773 | Find the magnitude of the vector $ \| \vec{v} \| = \left(4,~7\right) $ . | 1 |
5774 | Find the magnitude of the vector $ \| \vec{v} \| = \left(8,~-2,~1\right) $ . | 1 |
5775 | Find the angle between vectors $ \left(-4,~-5\right)$ and $\left(-1,~2\right)$. | 1 |
5776 | Find the magnitude of the vector $ \| \vec{v} \| = \left(5,~3\right) $ . | 1 |
5777 | Find the magnitude of the vector $ \| \vec{v} \| = \left(2,~3\right) $ . | 1 |
5778 | Find the difference of the vectors $ \vec{v_1} = \left(-5,~7\right) $ and $ \vec{v_2} = \left(-7,~4\right) $ . | 1 |
5779 | Find the projection of the vector $ \vec{v_1} = \left(-1,~1,~2\right) $ on the vector $ \vec{v_2} = \left(-2,~10,~10\right) $. | 1 |
5780 | Find the difference of the vectors $ \vec{v_1} = \left(3,~-3\right) $ and $ \vec{v_2} = \left(0,~-6\right) $ . | 1 |
5781 | Calculate the cross product of the vectors $ \vec{v_1} = \left(0,~\dfrac{ 1 }{ 2 },~0\right) $ and $ \vec{v_2} = \left(1,~1,~0\right) $ . | 1 |
5782 | Calculate the dot product of the vectors $ \vec{v_1} = \left(5,~-1\right) $ and $ \vec{v_2} = \left(3,~5\right) $ . | 1 |
5783 | Calculate the dot product of the vectors $ \vec{v_1} = \left(5.2,~2.5,~-4.5\right) $ and $ \vec{v_2} = \left(-3,~4,~-1.25\right) $ . | 1 |
5784 | Find the sum of the vectors $ \vec{v_1} = \left(-8,~5\right) $ and $ \vec{v_2} = \left(8,~-4\right) $ . | 1 |
5785 | Find the magnitude of the vector $ \| \vec{v} \| = \left(2000,~0,~0\right) $ . | 1 |
5786 | Find the angle between vectors $ \left(-10,~0,~6\right)$ and $\left(1,~3,~5\right)$. | 1 |
5787 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-1,~-4,~1\right) $ . | 1 |
5788 | Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~3\right) $ and $ \vec{v_2} = \left(-3,~-10\right) $ . | 1 |
5789 | Find the sum of the vectors $ \vec{v_1} = \left(-3,~3\right) $ and $ \vec{v_2} = \left(5,~2\right) $ . | 1 |
5790 | Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~3,~1\right) $ and $ \vec{v_2} = \left(3,~1,~-1\right) $ . | 1 |
5791 | Find the projection of the vector $ \vec{v_1} = \left(-2,~10,~20\right) $ on the vector $ \vec{v_2} = \left(-1,~1,~2\right) $. | 1 |
5792 | Find the difference of the vectors $ \vec{v_1} = \left(3,~3\right) $ and $ \vec{v_2} = \left(-1,~1\right) $ . | 1 |
5793 | Find the magnitude of the vector $ \| \vec{v} \| = \left(2.9,~3.07\right) $ . | 1 |
5794 | Find the angle between vectors $ \left(3,~0\right)$ and $\left(9,~2\right)$. | 1 |
5795 | Find the sum of the vectors $ \vec{v_1} = \left(1,~1\right) $ and $ \vec{v_2} = \left(2,~5\right) $ . | 1 |
5796 | Determine whether the vectors $ \vec{v_1} = \left(9,~-7\right) $ and $ \vec{v_2} = \left(9,~-7\right) $ are linearly independent or dependent. | 1 |
5797 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-1,~-5\right) $ . | 1 |
5798 | Calculate the dot product of the vectors $ \vec{v_1} = \left(9,~8,~-10\right) $ and $ \vec{v_2} = \left(16,~-38,~-40\right) $ . | 1 |
5799 | Calculate the cross product of the vectors $ \vec{v_1} = \left(8,~-2,~1\right) $ and $ \vec{v_2} = \left(-2,~1,~0\right) $ . | 1 |
5800 | Find the magnitude of the vector $ \| \vec{v} \| = \left(1,~2,~2\right) $ . | 1 |