Vectors
(the database of solved problems)
All the problems and solutions shown below were generated using the Vectors Calculator.
| ID |
Problem |
Count |
| 5751 | Determine whether the vectors $ \vec{v_1} = \left(12,~-9,~6\right) $, $ \vec{v_2} = \left(-8,~6,~-4\right) $ and $ \vec{v_3} = \left(0,~0,~0\right)$ are linearly independent or dependent. | 1 |
| 5752 | Find the angle between vectors $ \left(12,~-9,~6\right)$ and $\left(-8,~6,~-4\right)$. | 1 |
| 5753 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~1,~1\right) $ and $ \vec{v_2} = \left(1,~0,~-1\right) $ . | 1 |
| 5754 | Determine whether the vectors $ \vec{v_1} = \left(1,~1,~1\right) $, $ \vec{v_2} = \left(1,~0,~-1\right) $ and $ \vec{v_3} = \left(0,~0,~0\right)$ are linearly independent or dependent. | 1 |
| 5755 | Find the sum of the vectors $ \vec{v_1} = \left(-3,~5\right) $ and $ \vec{v_2} = \left(-2,~2\right) $ . | 1 |
| 5756 | Calculate the cross product of the vectors $ \vec{v_1} = \left(5,~1,~-5\right) $ and $ \vec{v_2} = \left(1,~0,~8\right) $ . | 1 |
| 5757 | Find the projection of the vector $ \vec{v_1} = \left(1,~4,~5\right) $ on the vector $ \vec{v_2} = \left(9,~0,~-1\right) $. | 1 |
| 5758 | Find the angle between vectors $ \left(-4,~7\right)$ and $\left(28,~-49\right)$. | 1 |
| 5759 | Find the angle between vectors $ \left(-2,~-1,~4\right)$ and $\left(\dfrac{ 2 }{ 3 },~\dfrac{ 1 }{ 3 },~-12\right)$. | 1 |
| 5760 | Find the angle between vectors $ \left(-2,~-1,~4\right)$ and $\left(\dfrac{ 1 }{ 3 },~\dfrac{ 1 }{ 3 },~-12\right)$. | 1 |
| 5761 | Find the angle between vectors $ \left(-2,~-1,~4\right)$ and $\left(\dfrac{ 2 }{ 3 },~-\dfrac{ 1 }{ 3 },~-12\right)$. | 1 |
| 5762 | Find the angle between vectors $ \left(-2,~-1,~4\right)$ and $\left(6,~3,~-12\right)$. | 1 |
| 5763 | Find the angle between vectors $ \left(-2,~4,~4\right)$ and $\left(2,~-2,~3\right)$. | 1 |
| 5764 | Find the angle between vectors $ \left(-4,~1,~1\right)$ and $\left(1,~19,~0\right)$. | 1 |
| 5765 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-2,~-3\right) $ and $ \vec{v_2} = \left(1,~5\right) $ . | 1 |
| 5766 | Find the sum of the vectors $ \vec{v_1} = \left(-2,~-3\right) $ and $ \vec{v_2} = \left(1,~5\right) $ . | 1 |
| 5767 | Find the difference of the vectors $ \vec{v_1} = \left(-2,~-3\right) $ and $ \vec{v_2} = \left(1,~5\right) $ . | 1 |
| 5768 | Find the difference of the vectors $ \vec{v_1} = \left(1,~5\right) $ and $ \vec{v_2} = \left(-2,~-3\right) $ . | 1 |
| 5769 | Calculate the dot product of the vectors $ \vec{v_1} = \left(2.5,~0.6\right) $ and $ \vec{v_2} = \left(-6,~4\right) $ . | 1 |
| 5770 | Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~1,~0.3333\right) $ and $ \vec{v_2} = \left(6,~-3,~-6\right) $ . | 1 |
| 5771 | Find the sum of the vectors $ \vec{v_1} = \left(0,~6\right) $ and $ \vec{v_2} = \left(-8,~0\right) $ . | 1 |
| 5772 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-0.8,~0.6\right) $ . | 1 |
| 5773 | Calculate the dot product of the vectors $ \vec{v_1} = \left(9,~-4\right) $ and $ \vec{v_2} = \left(7,~6\right) $ . | 1 |
| 5774 | Find the sum of the vectors $ \vec{v_1} = \left(4,~-5\right) $ and $ \vec{v_2} = \left(-2,~7\right) $ . | 1 |
| 5775 | Find the difference of the vectors $ \vec{v_1} = \left(-2,~0,~-3\right) $ and $ \vec{v_2} = \left(-4,~-6,~1\right) $ . | 1 |
| 5776 | Find the difference of the vectors $ \vec{v_1} = \left(3,~7,~19\right) $ and $ \vec{v_2} = \left(6,~16,~13\right) $ . | 1 |
| 5777 | Calculate the cross product of the vectors $ \vec{v_1} = \left(2,~-1,~6\right) $ and $ \vec{v_2} = \left(2,~2,~1\right) $ . | 1 |
| 5778 | Calculate the cross product of the vectors $ \vec{v_1} = \left(2,~2,~1\right) $ and $ \vec{v_2} = \left(2,~-1,~6\right) $ . | 1 |
| 5779 | Find the sum of the vectors $ \vec{v_1} = \left(2,~3\right) $ and $ \vec{v_2} = \left(6,~6\right) $ . | 1 |
| 5780 | Calculate the dot product of the vectors $ \vec{v_1} = \left(4,~-5,~-4\right) $ and $ \vec{v_2} = \left(0,~-4,~-5\right) $ . | 1 |
| 5781 | Calculate the dot product of the vectors $ \vec{v_1} = \left(4,~-5,~-4\right) $ and $ \vec{v_2} = \left(-3,~1,~2\right) $ . | 1 |
| 5782 | Find the angle between vectors $ \left(3,~-5,~-7\right)$ and $\left(1,~-3,~2\right)$. | 1 |
| 5783 | Calculate the cross product of the vectors $ \vec{v_1} = \left(2,~1,~0\right) $ and $ \vec{v_2} = \left(-3,~2,~0\right) $ . | 1 |
| 5784 | Find the magnitude of the vector $ \| \vec{v} \| = \left(2,~1,~0\right) $ . | 1 |
| 5785 | Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~1,~0\right) $ and $ \vec{v_2} = \left(-3,~2,~0\right) $ . | 1 |
| 5786 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-3,~2,~0\right) $ and $ \vec{v_2} = \left(2,~1,~0\right) $ . | 1 |
| 5787 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-3,~2,~0\right) $ and $ \vec{v_2} = \left(1,~4,~-2\right) $ . | 1 |
| 5788 | Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~1,~0\right) $ and $ \vec{v_2} = \left(-4,~-6,~-14\right) $ . | 1 |
| 5789 | Find the magnitude of the vector $ \| \vec{v} \| = \left(\dfrac{ 26 }{ 5 },~-\dfrac{ 43 }{ 10 }\right) $ . | 1 |
| 5790 | Determine whether the vectors $ \vec{v_1} = \left(-2,~6\right) $ and $ \vec{v_2} = \left(-9,~-3\right) $ are linearly independent or dependent. | 1 |
| 5791 | Find the magnitude of the vector $ \| \vec{v} \| = \left(4,~-2\right) $ . | 1 |
| 5792 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-1,~-4,~3\right) $ . | 1 |
| 5793 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-3,~-4\right) $ and $ \vec{v_2} = \left(0,~0\right) $ . | 1 |
| 5794 | Find the angle between vectors $ \left(-3,~-4\right)$ and $\left(-6,~-8\right)$. | 1 |
| 5795 | Find the magnitude of the vector $ \| \vec{v} \| = \left(0,~0,~11\right) $ . | 1 |
| 5796 | Find the magnitude of the vector $ \| \vec{v} \| = \left(0,~0,~11\right) $ . | 1 |
| 5797 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~-3,~-9\right) $ and $ \vec{v_2} = \left(-13,~-11,~5\right) $ . | 1 |
| 5798 | Find the sum of the vectors $ \vec{v_1} = \left(2,~5,~3\right) $ and $ \vec{v_2} = \left(4,~1,~2\right) $ . | 1 |
| 5799 | Find the projection of the vector $ \vec{v_1} = \left(2,~5,~3\right) $ on the vector $ \vec{v_2} = \left(4,~1,~2\right) $. | 1 |
| 5800 | Find the angle between vectors $ \left(5,~5,~1\right)$ and $\left(-3,~4,~2\right)$. | 1 |
