Vectors
(the database of solved problems)
All the problems and solutions shown below were generated using the Vectors Calculator.
| ID |
Problem |
Count |
| 4151 | | 1 |
| 4152 | Find the projection of the vector $ \vec{v_1} = \left(1,~1,~1\right) $ on the vector $ \vec{v_2} = \left(1,~2,~3\right) $. | 1 |
| 4153 | Calculate the cross product of the vectors $ \vec{v_1} = \left(2,~2,~1\right) $ and $ \vec{v_2} = \left(2,~-1,~0\right) $ . | 1 |
| 4154 | Find the magnitude of the vector $ \| \vec{v} \| = \left(0,~0,~0\right) $ . | 1 |
| 4155 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-1,~0,~1\right) $ . | 1 |
| 4156 | Find the sum of the vectors $ \vec{v_1} = \left(-6,~8\right) $ and $ \vec{v_2} = \left(6,~3\right) $ . | 1 |
| 4157 | Find the difference of the vectors $ \vec{v_1} = \left(-6,~8\right) $ and $ \vec{v_2} = \left(6,~3\right) $ . | 1 |
| 4158 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-6,~8\right) $ . | 1 |
| 4159 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-12,~5\right) $ . | 1 |
| 4160 | Find the sum of the vectors $ \vec{v_1} = \left(9,~-4,~3\right) $ and $ \vec{v_2} = \left(3,~0,~-9\right) $ . | 1 |
| 4161 | Find the magnitude of the vector $ \| \vec{v} \| = \left(9,~-4,~3\right) $ . | 1 |
| 4162 | Find the difference of the vectors $ \vec{v_1} = \left(9,~-4,~3\right) $ and $ \vec{v_2} = \left(3,~0,~-9\right) $ . | 1 |
| 4163 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-1,~0,~-1\right) $ and $ \vec{v_2} = \left(1,~1,~1\right) $ . | 1 |
| 4164 | | 1 |
| 4165 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-1000,~0,~-3000\right) $ . | 1 |
| 4166 | Find the magnitude of the vector $ \| \vec{v} \| = \left(3,~4\right) $ . | 1 |
| 4167 | Calculate the cross product of the vectors $ \vec{v_1} = \left(0,~1,~0\right) $ and $ \vec{v_2} = \left(2,~2,~2\right) $ . | 1 |
| 4168 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~1,~1\right) $ and $ \vec{v_2} = \left(1,~1,~1\right) $ . | 1 |
| 4169 | Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~2,~\sqrt{ 5 }\right) $ and $ \vec{v_2} = \left(-3,~-4,~-\sqrt{ 5 }\right) $ . | 1 |
| 4170 | Find the angle between vectors $ \left(2,~-3,~2\right)$ and $\left(3,~-1,~4\right)$. | 1 |
| 4171 | Find the magnitude of the vector $ \| \vec{v} \| = \left(0,~0,~0\right) $ . | 1 |
| 4172 | Find the magnitude of the vector $ \| \vec{v} \| = \left(0,~-1,~0\right) $ . | 1 |
| 4173 | Find the magnitude of the vector $ \| \vec{v} \| = \left(1,~1,~1\right) $ . | 1 |
| 4174 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~1,~1\right) $ and $ \vec{v_2} = \left(1,~2,~1\right) $ . | 1 |
| 4175 | Determine whether the vectors $ \vec{v_1} = \left(1,~1\right) $ and $ \vec{v_2} = \left(1,~1\right) $ are linearly independent or dependent. | 1 |
| 4176 | Calculate the cross product of the vectors $ \vec{v_1} = \left(4,~3,~6\right) $ and $ \vec{v_2} = \left(-1,~3,~-8\right) $ . | 1 |
| 4177 | Calculate the cross product of the vectors $ \vec{v_1} = \left(5,~-1,~-2\right) $ and $ \vec{v_2} = \left(0,~0,~0\right) $ . | 1 |
| 4178 | Calculate the dot product of the vectors $ \vec{v_1} = \left(5,~-1,~-2\right) $ and $ \vec{v_2} = \left(0,~0,~0\right) $ . | 1 |
| 4179 | Calculate the dot product of the vectors $ \vec{v_1} = \left(0,~0,~0\right) $ and $ \vec{v_2} = \left(5,~-1,~-2\right) $ . | 1 |
| 4180 | Find the angle between vectors $ \left(0,~1,~0\right)$ and $\left(12,~1,~1\right)$. | 1 |
| 4181 | Find the angle between vectors $ \left(0,~1,~0\right)$ and $\left(0,~0,~1\right)$. | 1 |
| 4182 | Find the angle between vectors $ \left(0,~1,~0\right)$ and $\left(12,~0,~0\right)$. | 1 |
| 4183 | Find the angle between vectors $ \left(0,~1,~0\right)$ and $\left(12,~2,~2\right)$. | 1 |
| 4184 | Find the angle between vectors $ \left(1,~2,~-3\right)$ and $\left(-2,~-4,~6\right)$. | 1 |
| 4185 | Find the angle between vectors $ \left(1,~1,~1\right)$ and $\left(2,~2,~2\right)$. | 1 |
| 4186 | Find the magnitude of the vector $ \| \vec{v} \| = \left(6,~7,~3\right) $ . | 1 |
| 4187 | Calculate the dot product of the vectors $ \vec{v_1} = \left(9,~6\right) $ and $ \vec{v_2} = \left(-4,~5\right) $ . | 1 |
| 4188 | | 1 |
| 4189 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-8,~12,~4\right) $ and $ \vec{v_2} = \left(6,~-9,~-3\right) $ . | 1 |
| 4190 | Find the angle between vectors $ \left(-8,~12,~4\right)$ and $\left(6,~-9,~-3\right)$. | 1 |
| 4191 | Find the angle between vectors $ \left(4,~-1,~4\right)$ and $\left(3,~4,~-2\right)$. | 1 |
| 4192 | Calculate the dot product of the vectors $ \vec{v_1} = \left(4,~5,~0\right) $ and $ \vec{v_2} = \left(1,~0,~9\right) $ . | 1 |
| 4193 | Calculate the cross product of the vectors $ \vec{v_1} = \left(4,~5,~0\right) $ and $ \vec{v_2} = \left(1,~0,~9\right) $ . | 1 |
| 4194 | Calculate the dot product of the vectors $ \vec{v_1} = \left(45,~-36,~-5\right) $ and $ \vec{v_2} = \left(4,~5,~0\right) $ . | 1 |
| 4195 | Calculate the dot product of the vectors $ \vec{v_1} = \left(45,~-36,~-5\right) $ and $ \vec{v_2} = \left(1,~0,~9\right) $ . | 1 |
| 4196 | Calculate the cross product of the vectors $ \vec{v_1} = \left(7,~6,~-5\right) $ and $ \vec{v_2} = \left(2,~-1,~1\right) $ . | 1 |
| 4197 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~-17,~-19\right) $ and $ \vec{v_2} = \left(1,~0,~9\right) $ . | 1 |
| 4198 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~-17,~-19\right) $ and $ \vec{v_2} = \left(2,~-1,~1\right) $ . | 1 |
| 4199 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~0,~-4\right) $ and $ \vec{v_2} = \left(0,~1,~1\right) $ . | 1 |
| 4200 | Calculate the cross product of the vectors $ \vec{v_1} = \left(7,~5,~1\right) $ and $ \vec{v_2} = \left(-1,~1,~0\right) $ . | 1 |
