Vectors
(the database of solved problems)
All the problems and solutions shown below were generated using the Vectors Calculator.
| ID |
Problem |
Count |
| 4101 | Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~-6,~-1\right) $ and $ \vec{v_2} = \left(11,~5,~9\right) $ . | 1 |
| 4102 | Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~-6,~-1\right) $ and $ \vec{v_2} = \left(7,~-11,~9\right) $ . | 1 |
| 4103 | Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~-6,~-1\right) $ and $ \vec{v_2} = \left(11,~5,~-9\right) $ . | 1 |
| 4104 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-1,~-10,~-2\right) $ . | 1 |
| 4105 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-1,~-10,~-2\right) $ and $ \vec{v_2} = \left(0,~0,~0\right) $ . | 1 |
| 4106 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-1,~-10,~-2\right) $ and $ \vec{v_2} = \left(0,~0,~0\right) $ . | 1 |
| 4107 | Find the difference of the vectors $ \vec{v_1} = \left(-3,~5\right) $ and $ \vec{v_2} = \left(6,~-2\right) $ . | 1 |
| 4108 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-4,~-6,~-\dfrac{ 2 }{ 3 }\right) $ and $ \vec{v_2} = \left(4,~-3,~1\right) $ . | 1 |
| 4109 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-2,~-1,~-3\right) $ and $ \vec{v_2} = \left(-1,~-2,~\dfrac{ 2 }{ 3 }\right) $ . | 1 |
| 4110 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-2,~-1,~-3\right) $ and $ \vec{v_2} = \left(-1,~-2,~\dfrac{ 2 }{ 3 }\right) $ . | 1 |
| 4111 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-4,~-6,~-\dfrac{ 2 }{ 3 }\right) $ and $ \vec{v_2} = \left(4,~-3,~-1\right) $ . | 1 |
| 4112 | Find the magnitude of the vector $ \| \vec{v} \| = \left(3,~8\right) $ . | 1 |
| 4113 | Find the magnitude of the vector $ \| \vec{v} \| = \left(12,~3\right) $ . | 1 |
| 4114 | Find the angle between vectors $ \left(1,~5,~3\right)$ and $\left(-3,~2,~-5\right)$. | 1 |
| 4115 | Find the magnitude of the vector $ \| \vec{v} \| = \left(1,~5,~3\right) $ . | 1 |
| 4116 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~2,~3\right) $ and $ \vec{v_2} = \left(-1,~2,~4\right) $ . | 1 |
| 4117 | Find the angle between vectors $ \left(1,~2,~3\right)$ and $\left(-1,~2,~4\right)$. | 1 |
| 4118 | Determine whether the vectors $ \vec{v_1} = \left(1,~2,~3\right) $, $ \vec{v_2} = \left(-1,~2,~4\right) $ and $ \vec{v_3} = \left(1,~5,~8\right)$ are linearly independent or dependent. | 1 |
| 4119 | Find the projection of the vector $ \vec{v_1} = \left(1,~2,~3\right) $ on the vector $ \vec{v_2} = \left(-1,~2,~4\right) $. | 1 |
| 4120 | | 1 |
| 4121 | Calculate the cross product of the vectors $ \vec{v_1} = \left(30,~0,~0\right) $ and $ \vec{v_2} = \left(0,~1,~0\right) $ . | 1 |
| 4122 | Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~2,~1\right) $ and $ \vec{v_2} = \left(1,~-2,~0\right) $ . | 1 |
| 4123 | Calculate the cross product of the vectors $ \vec{v_1} = \left(2,~2,~1\right) $ and $ \vec{v_2} = \left(1,~-2,~0\right) $ . | 1 |
| 4124 | Find the projection of the vector $ \vec{v_1} = \left(2,~2,~1\right) $ on the vector $ \vec{v_2} = \left(1,~-2,~0\right) $. | 1 |
| 4125 | Find the projection of the vector $ \vec{v_1} = \left(\dfrac{\sqrt{ 2 }}{ 2 },~\dfrac{\sqrt{ 2 }}{ 2 },~0\right) $ on the vector $ \vec{v_2} = \left(-1,~1,~-1\right) $. | 1 |
| 4126 | Calculate the dot product of the vectors $ \vec{v_1} = \left(\dfrac{\sqrt{ 2 }}{ 2 },~\dfrac{\sqrt{ 2 }}{ 2 },~0\right) $ and $ \vec{v_2} = \left(-1,~1,~-1\right) $ . | 1 |
| 4127 | Calculate the dot product of the vectors $ \vec{v_1} = \left(\dfrac{\sqrt{ 2 }}{ 2 },~\dfrac{\sqrt{ 2 }}{ 2 },~0\right) $ and $ \vec{v_2} = \left(0,~-2,~-2\right) $ . | 1 |
| 4128 | Find the projection of the vector $ \vec{v_1} = \left(\dfrac{\sqrt{ 2 }}{ 2 },~\dfrac{\sqrt{ 2 }}{ 2 },~0\right) $ on the vector $ \vec{v_2} = \left(0,~-2,~-2\right) $. | 1 |
| 4129 | Find the projection of the vector $ \vec{v_1} = \left(-1,~1,~-1\right) $ on the vector $ \vec{v_2} = \left(0,~-2,~-2\right) $. | 1 |
| 4130 | Find the projection of the vector $ \vec{v_1} = \left(1,~1\right) $ on the vector $ \vec{v_2} = \left(2,~0\right) $. | 1 |
| 4131 | | 1 |
| 4132 | Calculate the dot product of the vectors $ \vec{v_1} = \left(0,~-2,~1\right) $ and $ \vec{v_2} = \left(0,~3,~-3\right) $ . | 1 |
| 4133 | Calculate the dot product of the vectors $ \vec{v_1} = \left(0,~3,~-2\right) $ and $ \vec{v_2} = \left(-3,~5,~3\right) $ . | 1 |
| 4134 | Find the difference of the vectors $ \vec{v_1} = \left(-1,~2\right) $ and $ \vec{v_2} = \left(3,~0\right) $ . | 1 |
| 4135 | Find the projection of the vector $ \vec{v_1} = \left(0,~0,~0\right) $ on the vector $ \vec{v_2} = \left(0,~0,~0\right) $. | 1 |
| 4136 | | 1 |
| 4137 | Find the sum of the vectors $ \vec{v_1} = \left(5,~-2,~4\right) $ and $ \vec{v_2} = \left(-1,~3,~-1\right) $ . | 1 |
| 4138 | Find the magnitude of the vector $ \| \vec{v} \| = \left(2,~-1\right) $ . | 1 |
| 4139 | Find the projection of the vector $ \vec{v_1} = \left(1,~1,~5\right) $ on the vector $ \vec{v_2} = \left(1,~1,~3\right) $. | 1 |
| 4140 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~1,~5\right) $ and $ \vec{v_2} = \left(1,~1,~3\right) $ . | 1 |
| 4141 | Calculate the cross product of the vectors $ \vec{v_1} = \left(2,~-1,~3\right) $ and $ \vec{v_2} = \left(1,~3,~-1\right) $ . | 1 |
| 4142 | Calculate the cross product of the vectors $ \vec{v_1} = \left(2,~3,~0\right) $ and $ \vec{v_2} = \left(4,~1,~0\right) $ . | 1 |
| 4143 | Find the angle between vectors $ \left(12,~0\right)$ and $\left(15,~0\right)$. | 1 |
| 4144 | Find the magnitude of the vector $ \| \vec{v} \| = \left(1,~1,~1\right) $ . | 1 |
| 4145 | Find the magnitude of the vector $ \| \vec{v} \| = \left(43,~30\right) $ . | 1 |
| 4146 | Find the angle between vectors $ \left(800,~0,~0\right)$ and $\left(847,~0,~0\right)$. | 1 |
| 4147 | Find the sum of the vectors $ \vec{v_1} = \left(\dfrac{ 49 }{ 100 },~0\right) $ and $ \vec{v_2} = \left(\dfrac{ 27 }{ 500 },~\dfrac{ 12 }{ 25 }\right) $ . | 1 |
| 4148 | Calculate the dot product of the vectors $ \vec{v_1} = \left(0,~-4,~-3\right) $ and $ \vec{v_2} = \left(-4,~-3,~-2\right) $ . | 1 |
| 4149 | Calculate the dot product of the vectors $ \vec{v_1} = \left(0,~-3,~-2\right) $ and $ \vec{v_2} = \left(0,~-1,~-1\right) $ . | 1 |
| 4150 | Find the difference of the vectors $ \vec{v_1} = \left(2,~1\right) $ and $ \vec{v_2} = \left(4,~-3\right) $ . | 1 |
