Vectors
(the database of solved problems)
All the problems and solutions shown below were generated using the Vectors Calculator.
| ID |
Problem |
Count |
| 4801 | Calculate the cross product of the vectors $ \vec{v_1} = \left(5,~-1,~1\right) $ and $ \vec{v_2} = \left(3,~2,~-4\right) $ . | 1 |
| 4802 | Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~0,~3\right) $ and $ \vec{v_2} = \left(2,~8,~-4\right) $ . | 1 |
| 4803 | 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 |
| 4804 | Find the angle between vectors $ \left(3,~1\right)$ and $\left(2,~-4\right)$. | 1 |
| 4805 | Find the difference of the vectors $ \vec{v_1} = \left(-4,~3\right) $ and $ \vec{v_2} = \left(3,~1\right) $ . | 1 |
| 4806 | Find the sum of the vectors $ \vec{v_1} = \left(\dfrac{ 1 }{ 5 },~\dfrac{ 1 }{ 9 }\right) $ and $ \vec{v_2} = \left(\dfrac{ 4 }{ 5 },~\dfrac{ 8 }{ 9 }\right) $ . | 1 |
| 4807 | Find the sum of the vectors $ \vec{v_1} = \left(-4,~2,~-4\right) $ and $ \vec{v_2} = \left(-2,~9,~-2\right) $ . | 1 |
| 4808 | Find the difference of the vectors $ \vec{v_1} = \left(0,~0,~0\right) $ and $ \vec{v_2} = \left(0,~0,~0\right) $ . | 1 |
| 4809 | Find the difference of the vectors $ \vec{v_1} = \left(-4,~2,~-4\right) $ and $ \vec{v_2} = \left(-2,~9,~-2\right) $ . | 1 |
| 4810 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-4,~2,~-4\right) $ and $ \vec{v_2} = \left(-2,~9,~-2\right) $ . | 1 |
| 4811 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-4,~2,~-4\right) $ and $ \vec{v_2} = \left(-2,~9,~-2\right) $ . | 1 |
| 4812 | Find the projection of the vector $ \vec{v_1} = \left(-7,~3,~2\right) $ on the vector $ \vec{v_2} = \left(5,~0,~-1\right) $. | 1 |
| 4813 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-\dfrac{ 185 }{ 26 },~0,~\dfrac{ 37 }{ 26 }\right) $ . | 1 |
| 4814 | Calculate the dot product of the vectors $ \vec{v_1} = \left(5,~0,~-1\right) $ and $ \vec{v_2} = \left(-7,~3,~2\right) $ . | 1 |
| 4815 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~7,~1\right) $ and $ \vec{v_2} = \left(1,~10,~1\right) $ . | 1 |
| 4816 | Calculate the cross product of the vectors $ \vec{v_1} = \left(0,~4,~0\right) $ and $ \vec{v_2} = \left(\dfrac{ 353553 }{ 50000 },~\dfrac{ 353553 }{ 50000 },~0\right) $ . | 1 |
| 4817 | Calculate the cross product of the vectors $ \vec{v_1} = \left(0,~4,~0\right) $ and $ \vec{v_2} = \left(\dfrac{ 707107 }{ 100000 },~\dfrac{ 707107 }{ 100000 },~0\right) $ . | 1 |
| 4818 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-7,~3,~2\right) $ and $ \vec{v_2} = \left(5,~0,~-1\right) $ . | 1 |
| 4819 | Find the magnitude of the vector $ \| \vec{v} \| = \left(1,~-1,~-1\right) $ . | 1 |
| 4820 | Determine whether the vectors $ \vec{v_1} = \left(1,~-1,~-1\right) $, $ \vec{v_2} = \left(1,~3,~-5\right) $ and $ \vec{v_3} = \left(0,~0,~0\right)$ are linearly independent or dependent. | 1 |
| 4821 | Find the projection of the vector $ \vec{v_1} = \left(1,~1,~1\right) $ on the vector $ \vec{v_2} = \left(3,~4,~5\right) $. | 1 |
| 4822 | Find the angle between vectors $ \left(-1,~2\right)$ and $\left(1,~-1\right)$. | 1 |
| 4823 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-1,~2\right) $ and $ \vec{v_2} = \left(1,~-1\right) $ . | 1 |
| 4824 | Find the projection of the vector $ \vec{v_1} = \left(-1,~2\right) $ on the vector $ \vec{v_2} = \left(1,~-1\right) $. | 1 |
| 4825 | Find the magnitude of the vector $ \| \vec{v} \| = \left(50,~65,~80\right) $ . | 1 |
| 4826 | Find the angle between vectors $ \left(50,~65,~80\right)$ and $\left(23,~80,~65\right)$. | 1 |
| 4827 | Find the angle between vectors $ \left(4,~7,~-2\right)$ and $\left(3,~-1,~7\right)$. | 1 |
| 4828 | Find the angle between vectors $ \left(-6,~9,~3\right)$ and $\left(4,~-6,~-2\right)$. | 1 |
| 4829 | Find the difference of the vectors $ \vec{v_1} = \left(-2,~-4\right) $ and $ \vec{v_2} = \left(6,~14\right) $ . | 1 |
| 4830 | Calculate the dot product of the vectors $ \vec{v_1} = \left(5,~-2,~-4\right) $ and $ \vec{v_2} = \left(9,~-1,~12\right) $ . | 1 |
| 4831 | Calculate the cross product of the vectors $ \vec{v_1} = \left(5,~-2,~-4\right) $ and $ \vec{v_2} = \left(5,~-2,~-4\right) $ . | 1 |
| 4832 | Calculate the dot product of the vectors $ \vec{v_1} = \left(5,~-2,~-4\right) $ and $ \vec{v_2} = \left(5,~-2,~-4\right) $ . | 1 |
| 4833 | Calculate the dot product of the vectors $ \vec{v_1} = \left(5,~-2,~-4\right) $ and $ \vec{v_2} = \left(5,~-2,~-4\right) $ . | 1 |
| 4834 | Find the difference of the vectors $ \vec{v_1} = \left(\dfrac{ 17 }{ 5 },~\dfrac{ 271 }{ 100 }\right) $ and $ \vec{v_2} = \left(0,~\dfrac{ 87 }{ 20 }\right) $ . | 1 |
| 4835 | Find the difference of the vectors $ \vec{v_1} = \left(0,~\dfrac{ 87 }{ 20 }\right) $ and $ \vec{v_2} = \left(\dfrac{ 17 }{ 5 },~\dfrac{ 271 }{ 100 }\right) $ . | 1 |
| 4836 | Find the sum of the vectors $ \vec{v_1} = \left(2,~-3\right) $ and $ \vec{v_2} = \left(6,~55\right) $ . | 1 |
| 4837 | Find the sum of the vectors $ \vec{v_1} = \left(2,~-3\right) $ and $ \vec{v_2} = \left(6,~5\right) $ . | 1 |
| 4838 | Find the difference of the vectors $ \vec{v_1} = \left(8,~2\right) $ and $ \vec{v_2} = \left(11,~-6\right) $ . | 1 |
| 4839 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-1240,~2255,~-4140\right) $ . | 1 |
| 4840 | Find the magnitude of the vector $ \| \vec{v} \| = \left(0,~-8\right) $ . | 1 |
| 4841 | Find the magnitude of the vector $ \| \vec{v} \| = \left(0.0583,~0.9372,~0.3438\right) $ . | 1 |
| 4842 | | 1 |
| 4843 | Find the projection of the vector $ \vec{v_1} = \left(433.699,~-222.676,~1227.82\right) $ on the vector $ \vec{v_2} = \left(434.468,~-350.031,~1224.75\right) $. | 1 |
| 4844 | Find the angle between vectors $ \left(433.699,~-222.676,~1227.82\right)$ and $\left(434.468,~-350.031,~1224.75\right)$. | 1 |
| 4845 | Find the difference of the vectors $ \vec{v_1} = \left(2,~-3\right) $ and $ \vec{v_2} = \left(2,~3\right) $ . | 1 |
| 4846 | Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~5\right) $ and $ \vec{v_2} = \left(7,~-6\right) $ . | 1 |
| 4847 | Find the angle between vectors $ \left(0,~2\right)$ and $\left(0,~1\right)$. | 1 |
| 4848 | Find the angle between vectors $ \left(0,~2\right)$ and $\left(1,~0\right)$. | 1 |
| 4849 | Calculate the dot product of the vectors $ \vec{v_1} = \left(0,~1000\right) $ and $ \vec{v_2} = \left(15,~0\right) $ . | 1 |
| 4850 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1000,~0\right) $ and $ \vec{v_2} = \left(530,~15\right) $ . | 1 |
