Vectors
(the database of solved problems)
All the problems and solutions shown below were generated using the Vectors Calculator.
| ID |
Problem |
Count |
| 6101 | Calculate the cross product of the vectors $ \vec{v_1} = \left(3,~2,~-4\right) $ and $ \vec{v_2} = \left(-3,~1,~-3\right) $ . | 1 |
| 6102 | Calculate the cross product of the vectors $ \vec{v_1} = \left(3,~4,~4\right) $ and $ \vec{v_2} = \left(0,~1,~2\right) $ . | 1 |
| 6103 | Calculate the cross product of the vectors $ \vec{v_1} = \left(3,~-3,~1\right) $ and $ \vec{v_2} = \left(2,~-4,~1\right) $ . | 1 |
| 6104 | Calculate the cross product of the vectors $ \vec{v_1} = \left(2,~-4,~1\right) $ and $ \vec{v_2} = \left(3,~-3,~1\right) $ . | 1 |
| 6105 | Calculate the cross product of the vectors $ \vec{v_1} = \left(3,~-3,~1\right) $ and $ \vec{v_2} = \left(3,~-3,~1\right) $ . | 1 |
| 6106 | Calculate the cross product of the vectors $ \vec{v_1} = \left(2,~2,~1\right) $ and $ \vec{v_2} = \left(-1,~-4,~2\right) $ . | 1 |
| 6107 | Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~3,~-2\right) $ and $ \vec{v_2} = \left(8,~-5,~-6\right) $ . | 1 |
| 6108 | Find the sum of the vectors $ \vec{v_1} = \left(3,~3,~-2\right) $ and $ \vec{v_2} = \left(1,~-2,~3\right) $ . | 1 |
| 6109 | Find the angle between vectors $ \left(3,~9\right)$ and $\left(-9,~-5\right)$. | 1 |
| 6110 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-4,~-7\right) $ . | 1 |
| 6111 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-1,~2\right) $ and $ \vec{v_2} = \left(2,~4\right) $ . | 1 |
| 6112 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-1,~2\right) $ . | 1 |
| 6113 | Find the magnitude of the vector $ \| \vec{v} \| = \left(5 \sqrt{ 2 },~\sqrt{ 113 }\right) $ . | 1 |
| 6114 | Find the angle between vectors $ \left(1,~2\right)$ and $\left(-1,~4\right)$. | 1 |
| 6115 | Calculate the dot product of the vectors $ \vec{v_1} = \left(7,~-2\right) $ and $ \vec{v_2} = \left(-2,~-1\right) $ . | 1 |
| 6116 | Find the sum of the vectors $ \vec{v_1} = \left(3,~-8\right) $ and $ \vec{v_2} = \left(-5,~-3\right) $ . | 1 |
| 6117 | Find the magnitude of the vector $ \| \vec{v} \| = \left(0,~45\right) $ . | 1 |
| 6118 | Find the projection of the vector $ \vec{v_1} = \left(-9,~-2\right) $ on the vector $ \vec{v_2} = \left(-5,~-7\right) $. | 1 |
| 6119 | Find the angle between vectors $ \left(-11,~9\right)$ and $\left(-8,~-4\right)$. | 1 |
| 6120 | Find the magnitude of the vector $ \| \vec{v} \| = \left(2,~41\right) $ . | 1 |
| 6121 | Find the difference of the vectors $ \vec{v_1} = \left(5,~1\right) $ and $ \vec{v_2} = \left(6,~-7\right) $ . | 1 |
| 6122 | Find the sum of the vectors $ \vec{v_1} = \left(-8,~6\right) $ and $ \vec{v_2} = \left(5,~-1\right) $ . | 1 |
| 6123 | Find the angle between vectors $ \left(-24,~-32\right)$ and $\left(-6,~-8\right)$. | 1 |
| 6124 | Calculate the cross product of the vectors $ \vec{v_1} = \left(0,~2,~-3\right) $ and $ \vec{v_2} = \left(2,~6,~7\right) $ . | 1 |
| 6125 | Calculate the cross product of the vectors $ \vec{v_1} = \left(3,~2,~-1\right) $ and $ \vec{v_2} = \left(32,~-6,~-4\right) $ . | 1 |
| 6126 | Calculate the cross product of the vectors $ \vec{v_1} = \left(3,~2,~-1\right) $ and $ \vec{v_2} = \left(0,~2,~-3\right) $ . | 1 |
| 6127 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-4,~9,~6\right) $ and $ \vec{v_2} = \left(2,~6,~7\right) $ . | 1 |
| 6128 | Find the angle between vectors $ \left(3,~-1,~-4\right)$ and $\left(6,~-2,~-8\right)$. | 1 |
| 6129 | Find the magnitude of the vector $ \| \vec{v} \| = \left(0,~-34.47,~-28.93\right) $ . | 1 |
| 6130 | Find the projection of the vector $ \vec{v_1} = \left(0.1667,~0.125\right) $ on the vector $ \vec{v_2} = \left(0.125,~0.875\right) $. | 1 |
| 6131 | Find the difference of the vectors $ \vec{v_1} = \left(-5,~-1\right) $ and $ \vec{v_2} = \left(-3,~-4\right) $ . | 1 |
| 6132 | Find the sum of the vectors $ \vec{v_1} = \left(1,~2\right) $ and $ \vec{v_2} = \left(-2,~5\right) $ . | 1 |
| 6133 | Find the angle between vectors $ \left(2,~2,~3\right)$ and $\left(-5,~4,~3\right)$. | 1 |
| 6134 | Find the angle between vectors $ \left(0,~2,~-10\right)$ and $\left(0,~-4,~-4\right)$. | 1 |
| 6135 | Calculate the cross product of the vectors $ \vec{v_1} = \left(4,~0,~-3\right) $ and $ \vec{v_2} = \left(-2,~0,~-5\right) $ . | 1 |
| 6136 | Calculate the cross product of the vectors $ \vec{v_1} = \left(3,~5,~-6\right) $ and $ \vec{v_2} = \left(1,~-3,~5\right) $ . | 1 |
| 6137 | Calculate the cross product of the vectors $ \vec{v_1} = \left(3,~5,~-6\right) $ and $ \vec{v_2} = \left(3,~5,~-6\right) $ . | 1 |
| 6138 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~-3,~5\right) $ and $ \vec{v_2} = \left(3,~5,~-6\right) $ . | 1 |
| 6139 | Calculate the cross product of the vectors $ \vec{v_1} = \left(3,~5,~-6\right) $ and $ \vec{v_2} = \left(-5,~15,~-25\right) $ . | 1 |
| 6140 | Find the sum of the vectors $ \vec{v_1} = \left(3,~5,~-6\right) $ and $ \vec{v_2} = \left(1,~-3,~5\right) $ . | 1 |
| 6141 | Find the sum of the vectors $ \vec{v_1} = \left(4,~2,~-1\right) $ and $ \vec{v_2} = \left(1,~-3,~5\right) $ . | 1 |
| 6142 | Calculate the cross product of the vectors $ \vec{v_1} = \left(4,~2,~-1\right) $ and $ \vec{v_2} = \left(1,~-3,~5\right) $ . | 1 |
| 6143 | Calculate the dot product of the vectors $ \vec{v_1} = \left(4,~2,~-1\right) $ and $ \vec{v_2} = \left(1,~-3,~5\right) $ . | 1 |
| 6144 | Calculate the dot product of the vectors $ \vec{v_1} = \left(6,~-1\right) $ and $ \vec{v_2} = \left(2,~3\right) $ . | 1 |
| 6145 | Find the angle between vectors $ \left(6,~-1\right)$ and $\left(2,~3\right)$. | 1 |
| 6146 | Find the angle between vectors $ \left(26,~-1\right)$ and $\left(7,~5\right)$. | 1 |
| 6147 | Find the angle between vectors $ \left(2,~-1\right)$ and $\left(7,~5\right)$. | 1 |
| 6148 | Find the angle between vectors $ \left(0,~2,~14\right)$ and $\left(0,~-4,~-4\right)$. | 1 |
| 6149 | Find the magnitude of the vector $ \| \vec{v} \| = \left(11,~12,~22\right) $ . | 1 |
| 6150 | Find the angle between vectors $ \left(0,~2,~10\right)$ and $\left(0,~4,~4\right)$. | 1 |
