Vectors
(the database of solved problems)
All the problems and solutions shown below were generated using the Vectors Calculator.
| ID |
Problem |
Count |
| 4251 | Find the magnitude of the vector $ \| \vec{v} \| = \left(2,~3\right) $ . | 1 |
| 4252 | Find the magnitude of the vector $ \| \vec{v} \| = \left(2,~7,~5\right) $ . | 1 |
| 4253 | Find the angle between vectors $ \left(2,~7,~5\right)$ and $\left(2,~7,~0\right)$. | 1 |
| 4254 | Calculate the cross product of the vectors $ \vec{v_1} = \left(2,~7,~5\right) $ and $ \vec{v_2} = \left(1,~-2,~3\right) $ . | 1 |
| 4255 | Calculate the cross product of the vectors $ \vec{v_1} = \left(2,~-3,~1\right) $ and $ \vec{v_2} = \left(-2,~1,~1\right) $ . | 1 |
| 4256 | | 1 |
| 4257 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~2,~3\right) $ and $ \vec{v_2} = \left(1,~1,~2\right) $ . | 1 |
| 4258 | Find the angle between vectors $ \left(-5,~2\right)$ and $\left(7,~-1\right)$. | 1 |
| 4259 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~2,~3\right) $ and $ \vec{v_2} = \left(3,~0,~6\right) $ . | 1 |
| 4260 | Determine whether the vectors $ \vec{v_1} = \left(1,~2,~3\right) $, $ \vec{v_2} = \left(3,~0,~6\right) $ and $ \vec{v_3} = \left(7,~1,~9\right)$ are linearly independent or dependent. | 1 |
| 4261 | | 1 |
| 4262 | Calculate the cross product of the vectors $ \vec{v_1} = \left(0,~5,~0\right) $ and $ \vec{v_2} = \left(4,~0,~5\right) $ . | 1 |
| 4263 | Calculate the cross product of the vectors $ \vec{v_1} = \left(5,~0,~0\right) $ and $ \vec{v_2} = \left(4,~0,~5\right) $ . | 1 |
| 4264 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-\dfrac{ 3 }{ 5 },~-\dfrac{ 4 }{ 5 },~0\right) $ and $ \vec{v_2} = \left(4,~0,~5\right) $ . | 1 |
| 4265 | Find the difference of the vectors $ \vec{v_1} = \left(1,~2,~5\right) $ and $ \vec{v_2} = \left(-1,~-2,~0\right) $ . | 1 |
| 4266 | Find the angle between vectors $ \left(1,~2,~5\right)$ and $\left(-1,~-2,~0\right)$. | 1 |
| 4267 | Find the angle between vectors $ \left(1,~2,~0\right)$ and $\left(-1,~-3,~0\right)$. | 1 |
| 4268 | Find the magnitude of the vector $ \| \vec{v} \| = \left(4,~-4 \sqrt{ 3 }\right) $ . | 1 |
| 4269 | Find the angle between vectors $ \left(4,~-4 \sqrt{ 3 }\right)$ and $\left(1,~0\right)$. | 1 |
| 4270 | Find the angle between vectors $ \left(-1,~2\right)$ and $\left(-6,~-3\right)$. | 1 |
| 4271 | Find the angle between vectors $ \left(1,~1\right)$ and $\left(2,~3\right)$. | 1 |
| 4272 | Find the angle between vectors $ \left(4,~5\right)$ and $\left(0,~1\right)$. | 1 |
| 4273 | Find the projection of the vector $ \vec{v_1} = \left(2,~3,~4\right) $ on the vector $ \vec{v_2} = \left(0,~0,~0\right) $. | 1 |
| 4274 | Find the difference of the vectors $ \vec{v_1} = \left(-3,~1,~-5\right) $ and $ \vec{v_2} = \left(0,~-1,~2\right) $ . | 1 |
| 4275 | Find the sum of the vectors $ \vec{v_1} = \left(-3,~5\right) $ and $ \vec{v_2} = \left(3,~3\right) $ . | 1 |
| 4276 | Find the difference of the vectors $ \vec{v_1} = \left(-3,~5\right) $ and $ \vec{v_2} = \left(3,~3\right) $ . | 1 |
| 4277 | Find the magnitude of the vector $ \| \vec{v} \| = \left(3,~-4\right) $ . | 1 |
| 4278 | Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~0\right) $ and $ \vec{v_2} = \left(-3,~2\right) $ . | 1 |
| 4279 | Find the angle between vectors $ \left(2,~1\right)$ and $\left(1,~-4\right)$. | 1 |
| 4280 | Find the angle between vectors $ \left(-3,~5\right)$ and $\left(0,~1\right)$. | 1 |
| 4281 | Find the sum of the vectors $ \vec{v_1} = \left(45,~27\right) $ and $ \vec{v_2} = \left(12,~0\right) $ . | 1 |
| 4282 | Find the sum of the vectors $ \vec{v_1} = \left(2,~0\right) $ and $ \vec{v_2} = \left(30,~18\right) $ . | 1 |
| 4283 | Find the difference of the vectors $ \vec{v_1} = \left(2,~0\right) $ and $ \vec{v_2} = \left(30,~18\right) $ . | 1 |
| 4284 | Find the magnitude of the vector $ \| \vec{v} \| = \left(4,~4 \sqrt{ 3 }\right) $ . | 1 |
| 4285 | Find the angle between vectors $ \left(4,~4 \sqrt{ 3 }\right)$ and $\left(1,~0\right)$. | 1 |
| 4286 | Find the angle between vectors $ \left(2,~3\right)$ and $\left(0,~1\right)$. | 1 |
| 4287 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-24,~7\right) $ . | 1 |
| 4288 | Find the angle between vectors $ \left(-24,~7\right)$ and $\left(1,~0\right)$. | 1 |
| 4289 | Find the angle between vectors $ \left(-4,~-5\right)$ and $\left(-1,~2\right)$. | 1 |
| 4290 | Find the sum of the vectors $ \vec{v_1} = \left(-1,~4\right) $ and $ \vec{v_2} = \left(3,~2\right) $ . | 1 |
| 4291 | Find the difference of the vectors $ \vec{v_1} = \left(-1,~4\right) $ and $ \vec{v_2} = \left(3,~2\right) $ . | 1 |
| 4292 | Calculate the dot product of the vectors $ \vec{v_1} = \left(5,~0\right) $ and $ \vec{v_2} = \left(-2,~5\right) $ . | 1 |
| 4293 | Find the sum of the vectors $ \vec{v_1} = \left(-5,~2\right) $ and $ \vec{v_2} = \left(-3,~-5\right) $ . | 1 |
| 4294 | Calculate the cross product of the vectors $ \vec{v_1} = \left(2,~2,~2\right) $ and $ \vec{v_2} = \left(3,~0,~0\right) $ . | 1 |
| 4295 | Calculate the cross product of the vectors $ \vec{v_1} = \left(0,~6,~-6\right) $ and $ \vec{v_2} = \left(1,~1,~4\right) $ . | 1 |
| 4296 | Calculate the cross product of the vectors $ \vec{v_1} = \left(3,~0,~0\right) $ and $ \vec{v_2} = \left(1,~1,~4\right) $ . | 1 |
| 4297 | Calculate the cross product of the vectors $ \vec{v_1} = \left(2,~2,~2\right) $ and $ \vec{v_2} = \left(0,~-12,~3\right) $ . | 1 |
| 4298 | Calculate the cross product of the vectors $ \vec{v_1} = \left(3,~3,~-2\right) $ and $ \vec{v_2} = \left(-1,~-4,~2\right) $ . | 1 |
| 4299 | Find the projection of the vector $ \vec{v_1} = \left(7,~5\right) $ on the vector $ \vec{v_2} = \left(2,~6\right) $. | 1 |
| 4300 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-1,~-4,~2\right) $ and $ \vec{v_2} = \left(2,~2,~1\right) $ . | 1 |
