Vectors
(the database of solved problems)
All the problems and solutions shown below were generated using the Vectors Calculator.
| ID |
Problem |
Count |
| 6251 | Calculate the cross product of the vectors $ \vec{v_1} = \left(2,~3,~2\right) $ and $ \vec{v_2} = \left(-1,~4,~-3\right) $ . | 1 |
| 6252 | Find the angle between vectors $ \left(3,~2\right)$ and $\left(4,~2\right)$. | 1 |
| 6253 | Find the angle between vectors $ \left(-3,~2\right)$ and $\left(4,~6\right)$. | 1 |
| 6254 | Calculate the cross product of the vectors $ \vec{v_1} = \left(7,~4,~5\right) $ and $ \vec{v_2} = \left(2,~-3,~-5\right) $ . | 1 |
| 6255 | Calculate the cross product of the vectors $ \vec{v_1} = \left(4,~0,~-5\right) $ and $ \vec{v_2} = \left(0,~-3,~4\right) $ . | 1 |
| 6256 | Calculate the dot product of the vectors $ \vec{v_1} = \left(7,~5\right) $ and $ \vec{v_2} = \left(2,~1\right) $ . | 1 |
| 6257 | Find the angle between vectors $ \left(7,~5\right)$ and $\left(2,~1\right)$. | 1 |
| 6258 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-1,~-2\right) $ and $ \vec{v_2} = \left(-5,~3\right) $ . | 1 |
| 6259 | Find the magnitude of the vector $ \| \vec{v} \| = \left(3,~-3\right) $ . | 1 |
| 6260 | Find the magnitude of the vector $ \| \vec{v} \| = \left(1,~0,~10\right) $ . | 1 |
| 6261 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~0,~10\right) $ and $ \vec{v_2} = \left(5,~-5,~3\right) $ . | 1 |
| 6262 | Calculate the cross product of the vectors $ \vec{v_1} = \left(8,~8,~2\right) $ and $ \vec{v_2} = \left(5,~-5,~3\right) $ . | 1 |
| 6263 | Calculate the dot product of the vectors $ \vec{v_1} = \left(8,~8,~2\right) $ and $ \vec{v_2} = \left(5,~-5,~3\right) $ . | 1 |
| 6264 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-4,~1,~1\right) $ and $ \vec{v_2} = \left(-1,~-1,~-2\right) $ . | 1 |
| 6265 | Find the difference of the vectors $ \vec{v_1} = \left(-8,~26\right) $ and $ \vec{v_2} = \left(-19,~-3\right) $ . | 1 |
| 6266 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-8,~26\right) $ and $ \vec{v_2} = \left(-19,~-3\right) $ . | 1 |
| 6267 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-8,~26\right) $ . | 1 |
| 6268 | Find the sum of the vectors $ \vec{v_1} = \left(-8,~26\right) $ and $ \vec{v_2} = \left(-19,~-3\right) $ . | 1 |
| 6269 | Find the angle between vectors $ \left(-8,~26\right)$ and $\left(-19,~-3\right)$. | 1 |
| 6270 | Find the difference of the vectors $ \vec{v_1} = \left(1,~-2\right) $ and $ \vec{v_2} = \left(-4,~2\right) $ . | 1 |
| 6271 | Find the angle between vectors $ \left(1,~4\right)$ and $\left(-2,~3\right)$. | 1 |
| 6272 | Find the projection of the vector $ \vec{v_1} = \left(\dfrac{ 53 }{ 100 },~\dfrac{ 47 }{ 100 }\right) $ on the vector $ \vec{v_2} = \left(\dfrac{ 7 }{ 20 },~\dfrac{ 13 }{ 20 }\right) $. | 1 |
| 6273 | Determine whether the vectors $ \vec{v_1} = \left(-3,~8\right) $ and $ \vec{v_2} = \left(8,~-3\right) $ are linearly independent or dependent. | 1 |
| 6274 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-3,~8\right) $ . | 1 |
| 6275 | Find the sum of the vectors $ \vec{v_1} = \left(4,~1\right) $ and $ \vec{v_2} = \left(-2,~3\right) $ . | 1 |
| 6276 | Find the angle between vectors $ \left(3,~0,~-1\right)$ and $\left(-5,~0,~-2\right)$. | 1 |
| 6277 | Find the angle between vectors $ \left(3,~0,~1\right)$ and $\left(6,~0,~2\right)$. | 1 |
| 6278 | Find the difference of the vectors $ \vec{v_1} = \left(-2,~4\right) $ and $ \vec{v_2} = \left(4,~-1\right) $ . | 1 |
| 6279 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-0.5614,~0.5614,~0\right) $ . | 1 |
| 6280 | Find the projection of the vector $ \vec{v_1} = \left(-0.5614,~0.5614,~0\right) $ on the vector $ \vec{v_2} = \left(0.4307,~-0.5614,~0\right) $. | 1 |
| 6281 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-1,~0,~1\right) $ . | 1 |
| 6282 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-8,~-5\right) $ . | 1 |
| 6283 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~0\right) $ and $ \vec{v_2} = \left(-1,~0\right) $ . | 1 |
| 6284 | Find the angle between vectors $ \left(5,~11\right)$ and $\left(4,~-3\right)$. | 1 |
| 6285 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-6,~-2\right) $ . | 1 |
| 6286 | Find the sum of the vectors $ \vec{v_1} = \left(-10,~8\right) $ and $ \vec{v_2} = \left(4,~-11\right) $ . | 1 |
| 6287 | Find the sum of the vectors $ \vec{v_1} = \left(4,~-5\right) $ and $ \vec{v_2} = \left(-7,~4\right) $ . | 1 |
| 6288 | Find the projection of the vector $ \vec{v_1} = \left(0,~1,~1\right) $ on the vector $ \vec{v_2} = \left(2,~33,~-1\right) $. | 1 |
| 6289 | Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~-1\right) $ and $ \vec{v_2} = \left(-2,~5\right) $ . | 1 |
| 6290 | Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~7,~5\right) $ and $ \vec{v_2} = \left(2,~9,~4\right) $ . | 1 |
| 6291 | Calculate the cross product of the vectors $ \vec{v_1} = \left(3,~7,~5\right) $ and $ \vec{v_2} = \left(2,~9,~4\right) $ . | 1 |
| 6292 | Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~-34,~-2\right) $ and $ \vec{v_2} = \left(-2,~-3,~0\right) $ . | 1 |
| 6293 | Calculate the cross product of the vectors $ \vec{v_1} = \left(2,~-34,~-2\right) $ and $ \vec{v_2} = \left(-2,~-3,~0\right) $ . | 1 |
| 6294 | Find the angle between vectors $ \left(2,~-34,~-2\right)$ and $\left(-2,~-3,~0\right)$. | 1 |
| 6295 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~1,~-1\right) $ and $ \vec{v_2} = \left(2,~1,~-3\right) $ . | 1 |
| 6296 | Find the angle between vectors $ \left(1,~1,~0\right)$ and $\left(2,~0,~3\right)$. | 1 |
| 6297 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~1,~0\right) $ and $ \vec{v_2} = \left(2,~0,~3\right) $ . | 1 |
| 6298 | Find the sum of the vectors $ \vec{v_1} = \left(6,~3\right) $ and $ \vec{v_2} = \left(1,~2\right) $ . | 1 |
| 6299 | Find the sum of the vectors $ \vec{v_1} = \left(5,~3\right) $ and $ \vec{v_2} = \left(4,~4\right) $ . | 1 |
| 6300 | Find the angle between vectors $ \left(1,~2\right)$ and $\left(4,~7\right)$. | 1 |
