Vectors
(the database of solved problems)
All the problems and solutions shown below were generated using the Vectors Calculator.
| ID |
Problem |
Count |
| 4051 | Find the projection of the vector $ \vec{v_1} = \left(4,~-4\right) $ on the vector $ \vec{v_2} = \left(3,~2\right) $. | 1 |
| 4052 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-1,~-12\right) $ and $ \vec{v_2} = \left(-30,~24\right) $ . | 1 |
| 4053 | Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~-2\right) $ and $ \vec{v_2} = \left(-5,~1\right) $ . | 1 |
| 4054 | Find the angle between vectors $ \left(0,~-2\right)$ and $\left(-1,~0\right)$. | 1 |
| 4055 | Find the angle between vectors $ \left(0,~2\right)$ and $\left(-1,~0\right)$. | 1 |
| 4056 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-2,~-2\right) $ and $ \vec{v_2} = \left(6,~3\right) $ . | 1 |
| 4057 | Find the magnitude of the vector $ \| \vec{v} \| = \left(4,~1\right) $ . | 1 |
| 4058 | Find the angle between vectors $ \left(7,~6\right)$ and $\left(-5,~9\right)$. | 1 |
| 4059 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-2,~4\right) $ . | 1 |
| 4060 | | 1 |
| 4061 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-3,~3,~1\right) $ . | 1 |
| 4062 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-5,~5,~-1\right) $ and $ \vec{v_2} = \left(-2,~1,~-1\right) $ . | 1 |
| 4063 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-5,~5,~-1\right) $ and $ \vec{v_2} = \left(-2,~1,~-1\right) $ . | 1 |
| 4064 | Calculate the cross product of the vectors $ \vec{v_1} = \left(3,~4,~2\right) $ and $ \vec{v_2} = \left(-3,~-2,~4\right) $ . | 1 |
| 4065 | Calculate the cross product of the vectors $ \vec{v_1} = \left(2,~1,~-1\right) $ and $ \vec{v_2} = \left(1,~-1,~1\right) $ . | 1 |
| 4066 | Calculate the dot product of the vectors $ \vec{v_1} = \left(4,~-3\right) $ and $ \vec{v_2} = \left(3,~-3\right) $ . | 1 |
| 4067 | Find the angle between vectors $ \left(4,~-3\right)$ and $\left(3,~-3\right)$. | 1 |
| 4068 | Find the angle between vectors $ \left(-2,~-5,~0\right)$ and $\left(1,~-2,~-1\right)$. | 1 |
| 4069 | Find the angle between vectors $ \left(-2,~0,~-5\right)$ and $\left(1,~-2,~-1\right)$. | 1 |
| 4070 | Find the difference of the vectors $ \vec{v_1} = \left(330,~0\right) $ and $ \vec{v_2} = \left(190,~-120\right) $ . | 1 |
| 4071 | Find the sum of the vectors $ \vec{v_1} = \left(330,~0\right) $ and $ \vec{v_2} = \left(264,~-120\right) $ . | 1 |
| 4072 | Find the magnitude of the vector $ \| \vec{v} \| = \left(4,~2\right) $ . | 1 |
| 4073 | Find the magnitude of the vector $ \| \vec{v} \| = \left(6,~-2,~3\right) $ . | 1 |
| 4074 | Find the magnitude of the vector $ \| \vec{v} \| = \left(6,~-2,~3\right) $ . | 1 |
| 4075 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-2,~4\right) $ and $ \vec{v_2} = \left(-3,~3\right) $ . | 1 |
| 4076 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-4,~-2,~-5\right) $ and $ \vec{v_2} = \left(6,~2,~-7\right) $ . | 1 |
| 4077 | | 1 |
| 4078 | Find the magnitude of the vector $ \| \vec{v} \| = \left(4,~1,~0\right) $ . | 1 |
| 4079 | Find the projection of the vector $ \vec{v_1} = \left(4,~1,~0\right) $ on the vector $ \vec{v_2} = \left(-2,~5,~1\right) $. | 1 |
| 4080 | Determine whether the vectors $ \vec{v_1} = \left(4,~1,~0\right) $, $ \vec{v_2} = \left(-2,~5,~1\right) $ and $ \vec{v_3} = \left(1,~1,~3\right)$ are linearly independent or dependent. | 1 |
| 4081 | Find the angle between vectors $ \left(4,~1,~0\right)$ and $\left(-2,~5,~1\right)$. | 1 |
| 4082 | Find the projection of the vector $ \vec{v_1} = \left(2,~3,~4\right) $ on the vector $ \vec{v_2} = \left(1,~-1,~0\right) $. | 1 |
| 4083 | Calculate the cross product of the vectors $ \vec{v_1} = \left(5,~4,~3\right) $ and $ \vec{v_2} = \left(1,~0,~1\right) $ . | 1 |
| 4084 | Find the projection of the vector $ \vec{v_1} = \left(\dfrac{ 1 }{ 9 },~\dfrac{ 8 }{ 9 }\right) $ on the vector $ \vec{v_2} = \left(\dfrac{ 1 }{ 4 },~\dfrac{ 3 }{ 4 }\right) $. | 1 |
| 4085 | Find the projection of the vector $ \vec{v_1} = \left(\dfrac{ 1 }{ 9 },~\dfrac{ 1 }{ 4 }\right) $ on the vector $ \vec{v_2} = \left(\dfrac{ 8 }{ 9 },~\dfrac{ 3 }{ 4 }\right) $. | 1 |
| 4086 | Find the magnitude of the vector $ \| \vec{v} \| = \left(1,~1,~1\right) $ . | 1 |
| 4087 | Calculate the dot product of the vectors $ \vec{v_1} = \left(0,~1,~1\right) $ and $ \vec{v_2} = \left(0,~-2,~1\right) $ . | 1 |
| 4088 | Calculate the dot product of the vectors $ \vec{v_1} = \left(0,~5,~-2\right) $ and $ \vec{v_2} = \left(3,~-2,~2\right) $ . | 1 |
| 4089 | Calculate the dot product of the vectors $ \vec{v_1} = \left(0,~2,~0\right) $ and $ \vec{v_2} = \left(4,~-1,~-3\right) $ . | 1 |
| 4090 | Calculate the dot product of the vectors $ \vec{v_1} = \left(0,~4,~2\right) $ and $ \vec{v_2} = \left(0,~4,~4\right) $ . | 1 |
| 4091 | Calculate the dot product of the vectors $ \vec{v_1} = \left(0,~-4,~2\right) $ and $ \vec{v_2} = \left(-1,~-2,~2\right) $ . | 1 |
| 4092 | Find the sum of the vectors $ \vec{v_1} = \left(6,~9\right) $ and $ \vec{v_2} = \left(4,~3\right) $ . | 1 |
| 4093 | Find the difference of the vectors $ \vec{v_1} = \left(6,~9\right) $ and $ \vec{v_2} = \left(4,~3\right) $ . | 1 |
| 4094 | Calculate the cross product of the vectors $ \vec{v_1} = \left(8,~2,~-6\right) $ and $ \vec{v_2} = \left(-4,~-1,~3\right) $ . | 1 |
| 4095 | Find the magnitude of the vector $ \| \vec{v} \| = \left(16,~-6\right) $ . | 1 |
| 4096 | Find the angle between vectors $ \left(5,~17\right)$ and $\left(3,~-1\right)$. | 1 |
| 4097 | Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~0,~1\right) $ and $ \vec{v_2} = \left(-1,~-10,~2\right) $ . | 1 |
| 4098 | Calculate the cross product of the vectors $ \vec{v_1} = \left(2,~0,~1\right) $ and $ \vec{v_2} = \left(-1,~-10,~2\right) $ . | 1 |
| 4099 | Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~0,~1\right) $ and $ \vec{v_2} = \left(-2,~-11,~2\right) $ . | 1 |
| 4100 | Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~-6,~-1\right) $ and $ \vec{v_2} = \left(33,~21,~-27\right) $ . | 1 |
