Vectors – Solved Problems Database
All the problems and solutions shown below were generated using the Vectors Calculator.
ID |
Problem |
Count |
6101 | Find the magnitude of the vector $ \| \vec{v} \| = \left(1,~2,~1\right) $ . | 1 |
6102 | Find the angle between vectors $ \left(1,~2,~0\right)$ and $\left(-1,~-3,~0\right)$. | 1 |
6103 | Find the projection of the vector $ \vec{v_1} = \left(2,~-1,~4\right) $ on the vector $ \vec{v_2} = \left(0,~1,~-3\right) $. | 1 |
6104 | Find the angle between vectors $ \left(0,~5,~5\right)$ and $\left(3,~0,~-4\right)$. | 1 |
6105 | Find the sum of the vectors $ \vec{v_1} = \left(-7,~-1\right) $ and $ \vec{v_2} = \left(2,~2\right) $ . | 1 |
6106 | Find the difference of the vectors $ \vec{v_1} = \left(2,~11\right) $ and $ \vec{v_2} = \left(-6,~10\right) $ . | 1 |
6107 | Find the angle between vectors $ \left(2,~-1,~1\right)$ and $\left(2,~2,~-2\right)$. | 1 |
6108 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-\dfrac{ 13 }{ 5 },~\dfrac{ 9 }{ 2 }\right) $ and $ \vec{v_2} = \left(\dfrac{ 11 }{ 10 },~\dfrac{ 5 }{ 2 }\right) $ . | 1 |
6109 | Find the magnitude of the vector $ \| \vec{v} \| = \left(\dfrac{ 1 }{ 5 },~\dfrac{ 4 }{ 5 }\right) $ . | 1 |
6110 | Find the projection of the vector $ \vec{v_1} = \left(4,~-5\right) $ on the vector $ \vec{v_2} = \left(3,~-1\right) $. | 1 |
6111 | Find the angle between vectors $ \left(-4,~4,~0\right)$ and $\left(3,~10,~-4\right)$. | 1 |
6112 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-2,~2,~0\right) $ . | 1 |
6113 | Find the magnitude of the vector $ \| \vec{v} \| = \left(4,~5,~-2\right) $ . | 1 |
6114 | Find the angle between vectors $ \left(2,~-19\right)$ and $\left(20,~2\right)$. | 1 |
6115 | Find the sum of the vectors $ \vec{v_1} = \left(0,~6\right) $ and $ \vec{v_2} = \left(-8,~0\right) $ . | 1 |
6116 | Determine whether the vectors $ \vec{v_1} = \left(7,~-6\right) $ and $ \vec{v_2} = \left(4,~1\right) $ are linearly independent or dependent. | 1 |
6117 | Find the difference of the vectors $ \vec{v_1} = \left(0,~1,~3\right) $ and $ \vec{v_2} = \left(0,~0,~1\right) $ . | 1 |
6118 | Find the magnitude of the vector $ \| \vec{v} \| = \left(8,~-1\right) $ . | 1 |
6119 | Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~-1\right) $ and $ \vec{v_2} = \left(-1,~3\right) $ . | 1 |
6120 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-2,~8\right) $ . | 1 |
6121 | Find the projection of the vector $ \vec{v_1} = \left(3,~-8\right) $ on the vector $ \vec{v_2} = \left(3,~-8\right) $. | 1 |
6122 | Determine whether the vectors $ \vec{v_1} = \left(2,~7,~3\right) $, $ \vec{v_2} = \left(1,~5,~8\right) $ and $ \vec{v_3} = \left(0,~0,~0\right)$ are linearly independent or dependent. | 1 |
6123 | Find the angle between vectors $ \left(0,~7,~-6\right)$ and $\left(2,~0,~-9\right)$. | 1 |
6124 | Find the angle between vectors $ \left(3,~5,~-7\right)$ and $\left(-3,~4,~-2\right)$. | 1 |
6125 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-6,~-5\right) $ . | 1 |
6126 | Find the projection of the vector $ \vec{v_1} = \left(5,~-1\right) $ on the vector $ \vec{v_2} = \left(-1,~2\right) $. | 1 |
6127 | Find the sum of the vectors $ \vec{v_1} = \left(2,~-6,~4\right) $ and $ \vec{v_2} = \left(0,~2,~-1\right) $ . | 1 |
6128 | Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~3,~10\right) $ and $ \vec{v_2} = \left(7,~5,~0\right) $ . | 1 |
6129 | Find the angle between vectors $ \left(2,~-20\right)$ and $\left(19,~40\right)$. | 1 |
6130 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-3,~-4,~-3\right) $ and $ \vec{v_2} = \left(-3,~-4,~-3\right) $ . | 1 |
6131 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-0.8,~0.6\right) $ . | 1 |
6132 | Calculate the dot product of the vectors $ \vec{v_1} = \left(9,~8,~-17\right) $ and $ \vec{v_2} = \left(1,~-6,~-1\right) $ . | 1 |
6133 | Determine whether the vectors $ \vec{v_1} = \left(0,~1,~2\right) $, $ \vec{v_2} = \left(0,~-2,~4\right) $ and $ \vec{v_3} = \left(0,~5,~2\right)$ are linearly independent or dependent. | 1 |
6134 | Calculate the cross product of the vectors $ \vec{v_1} = \left(0,~-4,~0\right) $ and $ \vec{v_2} = \left(6,~-5,~2\right) $ . | 1 |
6135 | Calculate the dot product of the vectors $ \vec{v_1} = \left(4,~4,~2\right) $ and $ \vec{v_2} = \left(-2,~-2,~8\right) $ . | 1 |
6136 | Find the difference of the vectors $ \vec{v_1} = \left(5,~2\right) $ and $ \vec{v_2} = \left(2,~5\right) $ . | 1 |
6137 | Find the magnitude of the vector $ \| \vec{v} \| = \left(1,~5,~3\right) $ . | 1 |
6138 | Find the sum of the vectors $ \vec{v_1} = \left(3,~11\right) $ and $ \vec{v_2} = \left(3,~-4\right) $ . | 1 |
6139 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-1,~-1\right) $ and $ \vec{v_2} = \left(1,~-1\right) $ . | 1 |
6140 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~2,~2\right) $ and $ \vec{v_2} = \left(0,~1,~0\right) $ . | 1 |
6141 | Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~3\right) $ and $ \vec{v_2} = \left(2,~1\right) $ . | 1 |
6142 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~2,~1\right) $ and $ \vec{v_2} = \left(3,~2,~-1\right) $ . | 1 |
6143 | Find the sum of the vectors $ \vec{v_1} = \left(-2,~-1\right) $ and $ \vec{v_2} = \left(3,~-2\right) $ . | 1 |
6144 | Find the magnitude of the vector $ \| \vec{v} \| = \left(2,~2\right) $ . | 1 |
6145 | Find the angle between vectors $ \left(2,~-18\right)$ and $\left(19,~40\right)$. | 1 |
6146 | Calculate the dot product of the vectors $ \vec{v_1} = \left(102,~-102,~170\right) $ and $ \vec{v_2} = \left(3,~-3,~5\right) $ . | 1 |
6147 | Find the magnitude of the vector $ \| \vec{v} \| = \left(0,~0\right) $ . | 1 |
6148 | Find the angle between vectors $ \left(5,~6\right)$ and $\left(7,~1\right)$. | 1 |
6149 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-\dfrac{ 5 }{ 2 },~6\right) $ and $ \vec{v_2} = \left(-10,~24\right) $ . | 1 |
6150 | Find the angle between vectors $ \left(5,~0\right)$ and $\left(-1,~-1\right)$. | 1 |