Vectors
(the database of solved problems)
All the problems and solutions shown below were generated using the Vectors Calculator.
| ID |
Problem |
Count |
| 101 | Calculate the dot product of the vectors $ \vec{v_1} = \left(5,~8\right) $ and $ \vec{v_2} = \left(-9,~2\right) $ . | 4 |
| 102 | Find the magnitude of the vector $ \| \vec{v} \| = \left(3,~2\right) $ . | 4 |
| 103 | Find the projection of the vector $ \vec{v_1} = \left(0,~3\right) $ on the vector $ \vec{v_2} = \left(6,~3\right) $. | 4 |
| 104 | Find the magnitude of the vector $ \| \vec{v} \| = \left(7,~7\right) $ . | 4 |
| 105 | Find the sum of the vectors $ \vec{v_1} = \left(3,~4\right) $ and $ \vec{v_2} = \left(-7,~2\right) $ . | 4 |
| 106 | Find the magnitude of the vector $ \| \vec{v} \| = \left(6,~-1\right) $ . | 4 |
| 107 | Calculate the dot product of the vectors $ \vec{v_1} = \left(6,~-2\right) $ and $ \vec{v_2} = \left(6,~-2\right) $ . | 4 |
| 108 | Find the projection of the vector $ \vec{v_1} = \left(-10,~-7\right) $ on the vector $ \vec{v_2} = \left(-8,~4\right) $. | 4 |
| 109 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~2,~3\right) $ and $ \vec{v_2} = \left(-3,~-1,~2\right) $ . | 4 |
| 110 | Find the difference of the vectors $ \vec{v_1} = \left(0,~-16\right) $ and $ \vec{v_2} = \left(8,~-20\right) $ . | 4 |
| 111 | Find the projection of the vector $ \vec{v_1} = \left(8,~5\right) $ on the vector $ \vec{v_2} = \left(-9,~-2\right) $. | 4 |
| 112 | Calculate the dot product of the vectors $ \vec{v_1} = \left(6,~-1\right) $ and $ \vec{v_2} = \left(5,~7\right) $ . | 4 |
| 113 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~1\right) $ and $ \vec{v_2} = \left(1,~1\right) $ . | 4 |
| 114 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-3,~0\right) $ and $ \vec{v_2} = \left(2,~0\right) $ . | 4 |
| 115 | Find the projection of the vector $ \vec{v_1} = \left(3,~-5\right) $ on the vector $ \vec{v_2} = \left(0,~1\right) $. | 4 |
| 116 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-10,~2\right) $ and $ \vec{v_2} = \left(1,~5\right) $ . | 4 |
| 117 | Find the difference of the vectors $ \vec{v_1} = \left(-2,~4\right) $ and $ \vec{v_2} = \left(-3,~-3\right) $ . | 4 |
| 118 | Find the sum of the vectors $ \vec{v_1} = \left(2,~-5\right) $ and $ \vec{v_2} = \left(1,~4\right) $ . | 4 |
| 119 | Find the magnitude of the vector $ \| \vec{v} \| = \left(9,~7\right) $ . | 4 |
| 120 | Find the magnitude of the vector $ \| \vec{v} \| = \left(1,~-3\right) $ . | 4 |
| 121 | Find the angle between vectors $ \left(-7,~-5\right)$ and $\left(2,~-8\right)$. | 4 |
| 122 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-1,~4\right) $ . | 4 |
| 123 | Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~4\right) $ and $ \vec{v_2} = \left(0,~0\right) $ . | 4 |
| 124 | Find the angle between vectors $ \left(1,~3\right)$ and $\left(2,~-5\right)$. | 4 |
| 125 | Find the difference of the vectors $ \vec{v_1} = \left(-24,~21\right) $ and $ \vec{v_2} = \left(-2,~1\right) $ . | 4 |
| 126 | Find the angle between vectors $ \left(2,~1,~-4\right)$ and $\left(3,~-5,~2\right)$. | 4 |
| 127 | Find the angle between vectors $ \left(2,~1,~-4\right)$ and $\left(3,~-5,~2\right)$. | 4 |
| 128 | Find the angle between vectors $ \left(3,~4\right)$ and $\left(10,~4\right)$. | 4 |
| 129 | | 4 |
| 130 | Find the projection of the vector $ \vec{v_1} = \left(-5,~8\right) $ on the vector $ \vec{v_2} = \left(-6,~-7\right) $. | 4 |
| 131 | Find the magnitude of the vector $ \| \vec{v} \| = \left(9,~-7\right) $ . | 4 |
| 132 | Calculate the dot product of the vectors $ \vec{v_1} = \left(11,~1\right) $ and $ \vec{v_2} = \left(1,~11\right) $ . | 4 |
| 133 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-8,~-7\right) $ . | 4 |
| 134 | Find the difference of the vectors $ \vec{v_1} = \left(3,~4\right) $ and $ \vec{v_2} = \left(-1,~1\right) $ . | 4 |
| 135 | Find the magnitude of the vector $ \| \vec{v} \| = \left(6,~-5\right) $ . | 4 |
| 136 | Find the magnitude of the vector $ \| \vec{v} \| = \left(6,~2\right) $ . | 4 |
| 137 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-3,~6\right) $ . | 4 |
| 138 | Determine whether the vectors $ \vec{v_1} = \left(1,~2\right) $ and $ \vec{v_2} = \left(2,~5\right) $ are linearly independent or dependent. | 4 |
| 139 | Find the magnitude of the vector $ \| \vec{v} \| = \left(2,~4\right) $ . | 4 |
| 140 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-4,~-5\right) $ . | 4 |
| 141 | Find the angle between vectors $ \left(\dfrac{ 2 }{ 5 },~\dfrac{ 3 }{ 10 }\right)$ and $\left(-\dfrac{ 3 }{ 20 },~\dfrac{ 1 }{ 5 }\right)$. | 4 |
| 142 | Find the angle between vectors $ \left(2,~1,~-4\right)$ and $\left(3,~-5,~2\right)$. | 4 |
| 143 | Find the magnitude of the vector $ \| \vec{v} \| = \left(24,~-7\right) $ . | 4 |
| 144 | Find the difference of the vectors $ \vec{v_1} = \left(3,~-1\right) $ and $ \vec{v_2} = \left(-4,~-2\right) $ . | 4 |
| 145 | Find the sum of the vectors $ \vec{v_1} = \left(4,~2\right) $ and $ \vec{v_2} = \left(-8,~-2\right) $ . | 4 |
| 146 | Find the difference of the vectors $ \vec{v_1} = \left(2,~1\right) $ and $ \vec{v_2} = \left(1,~3\right) $ . | 4 |
| 147 | Find the sum of the vectors $ \vec{v_1} = \left(-5,~-3\right) $ and $ \vec{v_2} = \left(3,~-8\right) $ . | 4 |
| 148 | Find the magnitude of the vector $ \| \vec{v} \| = \left(1,~1\right) $ . | 4 |
| 149 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-1,~2\right) $ . | 4 |
| 150 | Find the sum of the vectors $ \vec{v_1} = \left(0,~1\right) $ and $ \vec{v_2} = \left(0,~1\right) $ . | 4 |
