Vectors
(the database of solved problems)
All the problems and solutions shown below were generated using the Vectors Calculator.
| ID |
Problem |
Count |
| 5101 | Find the magnitude of the vector $ \| \vec{v} \| = \left(\dfrac{ 1 }{ 10 },~\dfrac{ 2 }{ 5 },~\dfrac{ 1 }{ 5 }\right) $ . | 1 |
| 5102 | Find the projection of the vector $ \vec{v_1} = \left(-1,~1,~-2\right) $ on the vector $ \vec{v_2} = \left(-7,~1,~4\right) $. | 1 |
| 5103 | Find the projection of the vector $ \vec{v_1} = \left(-9,~1,~6\right) $ on the vector $ \vec{v_2} = \left(-7,~1,~4\right) $. | 1 |
| 5104 | Find the magnitude of the vector $ \| \vec{v} \| = \left(5,~6\right) $ . | 1 |
| 5105 | Find the difference of the vectors $ \vec{v_1} = \left(-2,~-4\right) $ and $ \vec{v_2} = \left(1,~3\right) $ . | 1 |
| 5106 | Find the angle between vectors $ \left(-2,~-4\right)$ and $\left(1,~3\right)$. | 1 |
| 5107 | Find the angle between vectors $ \left(\dfrac{\sqrt{ 3 }}{ 2 },~0.5\right)$ and $\left(- \dfrac{\sqrt{ 2 }}{ 2 },~- \dfrac{\sqrt{ 2 }}{ 2 }\right)$. | 1 |
| 5108 | Find the magnitude of the vector $ \| \vec{v} \| = \left(9,~40\right) $ . | 1 |
| 5109 | Find the angle between vectors $ \left(-3,~-9\right)$ and $\left(2,~-4\right)$. | 1 |
| 5110 | Find the angle between vectors $ \left(-2,~5\right)$ and $\left(9,~8\right)$. | 1 |
| 5111 | Find the angle between vectors $ \left(-1,~9\right)$ and $\left(5,~2\right)$. | 1 |
| 5112 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-\dfrac{ 9 }{ 41 },~\dfrac{ 40 }{ 41 }\right) $ . | 1 |
| 5113 | Find the angle between vectors $ \left(2,~7\right)$ and $\left(3,~0\right)$. | 1 |
| 5114 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~2,~3\right) $ and $ \vec{v_2} = \left(1,~-1,~1\right) $ . | 1 |
| 5115 | Find the magnitude of the vector $ \| \vec{v} \| = \left(7,~-8\right) $ . | 1 |
| 5116 | Find the magnitude of the vector $ \| \vec{v} \| = \left(0,~0\right) $ . | 1 |
| 5117 | Find the magnitude of the vector $ \| \vec{v} \| = \left(0,~0\right) $ . | 1 |
| 5118 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-5,~2\right) $ . | 1 |
| 5119 | Find the sum of the vectors $ \vec{v_1} = \left(-5,~2\right) $ and $ \vec{v_2} = \left(-6,~12\right) $ . | 1 |
| 5120 | Find the sum of the vectors $ \vec{v_1} = \left(-6,~-2,~0\right) $ and $ \vec{v_2} = \left(-3,~3,~0\right) $ . | 1 |
| 5121 | Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~-5\right) $ and $ \vec{v_2} = \left(-6,~-4\right) $ . | 1 |
| 5122 | Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~5\right) $ and $ \vec{v_2} = \left(0,~-4\right) $ . | 1 |
| 5123 | Find the projection of the vector $ \vec{v_1} = \left(\dfrac{ 8 }{ 3 },~\dfrac{ 8 }{ 3 }\right) $ on the vector $ \vec{v_2} = \left(7,~-7\right) $. | 1 |
| 5124 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-\dfrac{ 1 }{ 2 },~- \dfrac{\sqrt{ 3 }}{ 2 }\right) $ and $ \vec{v_2} = \left(\dfrac{\sqrt{ 2 }}{ 2 },~- \dfrac{\sqrt{ 2 }}{ 2 }\right) $ . | 1 |
| 5125 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~-\sqrt{ 3 }\right) $ and $ \vec{v_2} = \left(1,~\sqrt{ 3 }\right) $ . | 1 |
| 5126 | Find the projection of the vector $ \vec{v_1} = \left(1,~-\sqrt{ 3 }\right) $ on the vector $ \vec{v_2} = \left(1,~\sqrt{ 3 }\right) $. | 1 |
| 5127 | Find the angle between vectors $ \left(1,~-\sqrt{ 3 }\right)$ and $\left(1,~\sqrt{ 3 }\right)$. | 1 |
| 5128 | Find the magnitude of the vector $ \| \vec{v} \| = \left(4,~6,~4\right) $ . | 1 |
| 5129 | Find the projection of the vector $ \vec{v_1} = \left(4,~6,~4\right) $ on the vector $ \vec{v_2} = \left(1,~4,~8\right) $. | 1 |
| 5130 | Find the angle between vectors $ \left(-1,~-3\right)$ and $\left(-1,~4\right)$. | 1 |
| 5131 | Calculate the dot product of the vectors $ \vec{v_1} = \left(0,~0\right) $ and $ \vec{v_2} = \left(0,~0\right) $ . | 1 |
| 5132 | Find the angle between vectors $ \left(1,~1,~-2\right)$ and $\left(-1,~1,~0\right)$. | 1 |
| 5133 | Find the magnitude of the vector $ \| \vec{v} \| = \left(4,~6\right) $ . | 1 |
| 5134 | Find the magnitude of the vector $ \| \vec{v} \| = \left(3,~6\right) $ . | 1 |
| 5135 | Find the difference of the vectors $ \vec{v_1} = \left(-\dfrac{ 3 }{ 5 },~\dfrac{ 4 }{ 5 }\right) $ and $ \vec{v_2} = \left(5,~25\right) $ . | 1 |
| 5136 | Calculate the dot product of the vectors $ \vec{v_1} = \left(5,~-2\right) $ and $ \vec{v_2} = \left(10,~-4\right) $ . | 1 |
| 5137 | Find the magnitude of the vector $ \| \vec{v} \| = \left(10,~-4\right) $ . | 1 |
| 5138 | Calculate the dot product of the vectors $ \vec{v_1} = \left(10,~-4\right) $ and $ \vec{v_2} = \left(5,~-2\right) $ . | 1 |
| 5139 | Find the angle between vectors $ \left(7,~-1\right)$ and $\left(1,~4\right)$. | 1 |
| 5140 | Find the sum of the vectors $ \vec{v_1} = \left(3,~9\right) $ and $ \vec{v_2} = \left(-6,~-7\right) $ . | 1 |
| 5141 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-1,~2,~3\right) $ and $ \vec{v_2} = \left(0,~2,~1\right) $ . | 1 |
| 5142 | Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~-2,~4\right) $ and $ \vec{v_2} = \left(3,~-6,~-2\right) $ . | 1 |
| 5143 | Calculate the cross product of the vectors $ \vec{v_1} = \left(2,~2,~2\right) $ and $ \vec{v_2} = \left(3,~4,~4\right) $ . | 1 |
| 5144 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-3,~6\right) $ and $ \vec{v_2} = \left(-4,~-6\right) $ . | 1 |
| 5145 | Find the sum of the vectors $ \vec{v_1} = \left(-3,~6\right) $ and $ \vec{v_2} = \left(0,~0\right) $ . | 1 |
| 5146 | Calculate the dot product of the vectors $ \vec{v_1} = \left(0,~0\right) $ and $ \vec{v_2} = \left(-4,~-6\right) $ . | 1 |
| 5147 | Find the sum of the vectors $ \vec{v_1} = \left(0,~0,~14\right) $ and $ \vec{v_2} = \left(3,~0,~14\right) $ . | 1 |
| 5148 | Find the projection of the vector $ \vec{v_1} = \left(-4,~-5\right) $ on the vector $ \vec{v_2} = \left(-8,~5\right) $. | 1 |
| 5149 | Find the angle between vectors $ \left(-4,~-5\right)$ and $\left(-8,~5\right)$. | 1 |
| 5150 | Find the angle between vectors $ \left(1,~2,~-3\right)$ and $\left(4,~-5,~6\right)$. | 1 |
