Vectors – Solved Problems Database
All the problems and solutions shown below were generated using the Vectors Calculator.
ID |
Problem |
Count |
6251 | Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~-9\right) $ and $ \vec{v_2} = \left(-3,~6\right) $ . | 1 |
6252 | Find the angle between vectors $ \left(2,~2,~-1\right)$ and $\left(-4,~0,~-3\right)$. | 1 |
6253 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~3,~-1\right) $ and $ \vec{v_2} = \left(-3,~-9,~3\right) $ . | 1 |
6254 | Find the angle between vectors $ \left(0,~0,~3\right)$ and $\left(7,~0,~0\right)$. | 1 |
6255 | Find the difference of the vectors $ \vec{v_1} = \left(1,~-1\right) $ and $ \vec{v_2} = \left(-4,~-3\right) $ . | 1 |
6256 | Find the magnitude of the vector $ \| \vec{v} \| = \left(4,~-2\right) $ . | 1 |
6257 | Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~4,~-2\right) $ and $ \vec{v_2} = \left(2,~-1,~2\right) $ . | 1 |
6258 | Find the magnitude of the vector $ \| \vec{v} \| = \left(2,~4,~-2\right) $ . | 1 |
6259 | Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~-1,~1\right) $ and $ \vec{v_2} = \left(0,~-2,~2\right) $ . | 1 |
6260 | Find the sum of the vectors $ \vec{v_1} = \left(6,~-5,~-2\right) $ and $ \vec{v_2} = \left(8,~7,~0\right) $ . | 1 |
6261 | Determine whether the vectors $ \vec{v_1} = \left(1,~1,~2\right) $, $ \vec{v_2} = \left(1,~0,~1\right) $ and $ \vec{v_3} = \left(2,~1,~3\right)$ are linearly independent or dependent. | 1 |
6262 | Determine whether the vectors $ \vec{v_1} = \left(3,~-1\right) $ and $ \vec{v_2} = \left(-9,~3\right) $ are linearly independent or dependent. | 1 |
6263 | Determine whether the vectors $ \vec{v_1} = \left(-1,~2,~3\right) $, $ \vec{v_2} = \left(4,~1,~-2\right) $ and $ \vec{v_3} = \left(-14,~-1,~16\right)$ are linearly independent or dependent. | 1 |
6264 | Determine whether the vectors $ \vec{v_1} = \left(4,~3,~1\right) $, $ \vec{v_2} = \left(0,~0,~0\right) $ and $ \vec{v_3} = \left(0,~0,~0\right)$ are linearly independent or dependent. | 1 |
6265 | Determine whether the vectors $ \vec{v_1} = \left(1,~2\right) $ and $ \vec{v_2} = \left(-1,~3\right) $ are linearly independent or dependent. | 1 |
6266 | Find the projection of the vector $ \vec{v_1} = \left(4,~1,~2\right) $ on the vector $ \vec{v_2} = \left(3,~2,~4\right) $. | 1 |
6267 | Calculate the cross product of the vectors $ \vec{v_1} = \left(6,~-2,~1\right) $ and $ \vec{v_2} = \left(2,~5,~-1\right) $ . | 1 |
6268 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-2,~-2\right) $ and $ \vec{v_2} = \left(6,~3\right) $ . | 1 |
6269 | Calculate the dot product of the vectors $ \vec{v_1} = \left(0,~0,~1\right) $ and $ \vec{v_2} = \left(0,~0,~1\right) $ . | 1 |
6270 | Determine whether the vectors $ \vec{v_1} = \left(1,~0\right) $ and $ \vec{v_2} = \left(0,~1\right) $ are linearly independent or dependent. | 1 |
6271 | 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 |
6272 | Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~-8,~0\right) $ and $ \vec{v_2} = \left(-4,~4,~-1\right) $ . | 1 |
6273 | Calculate the cross product of the vectors $ \vec{v_1} = \left(2,~1,~-2\right) $ and $ \vec{v_2} = \left(3,~-4,~2\right) $ . | 1 |
6274 | Find the sum of the vectors $ \vec{v_1} = \left(9,~4,~0\right) $ and $ \vec{v_2} = \left(1,~6,~7\right) $ . | 1 |
6275 | Calculate the cross product of the vectors $ \vec{v_1} = \left(2,~0,~2\right) $ and $ \vec{v_2} = \left(0,~2,~2\right) $ . | 1 |
6276 | Find the projection of the vector $ \vec{v_1} = \left(89,~157\right) $ on the vector $ \vec{v_2} = \left(237,~326\right) $. | 1 |
6277 | Find the angle between vectors $ \left(3,~4,~-2\right)$ and $\left(2,~-1,~2\right)$. | 1 |
6278 | Find the magnitude of the vector $ \| \vec{v} \| = \left(3,~4\right) $ . | 1 |
6279 | Find the magnitude of the vector $ \| \vec{v} \| = \left(9,~40\right) $ . | 1 |
6280 | Find the difference of the vectors $ \vec{v_1} = \left(0,~-1\right) $ and $ \vec{v_2} = \left(-3,~5\right) $ . | 1 |
6281 | Find the magnitude of the vector $ \| \vec{v} \| = \left(3,~1,~2\right) $ . | 1 |
6282 | Calculate the cross product of the vectors $ \vec{v_1} = \left(4,~3,~1\right) $ and $ \vec{v_2} = \left(0,~0,~0\right) $ . | 1 |
6283 | Find the magnitude of the vector $ \| \vec{v} \| = \left(\dfrac{ 1 }{ 8 },~\dfrac{ 7 }{ 8 }\right) $ . | 1 |
6284 | Calculate the cross product of the vectors $ \vec{v_1} = \left(0,~0,~1\right) $ and $ \vec{v_2} = \left(0,~0,~1\right) $ . | 1 |
6285 | Determine whether the vectors $ \vec{v_1} = \left(1,~0,~0\right) $, $ \vec{v_2} = \left(1,~0,~1\right) $ and $ \vec{v_3} = \left(1,~1,~1\right)$ are linearly independent or dependent. | 1 |
6286 | Find the difference of the vectors $ \vec{v_1} = \left(2,~3\right) $ and $ \vec{v_2} = \left(4,~5\right) $ . | 1 |
6287 | Find the angle between vectors $ \left(-\dfrac{ 20 }{ 17 },~\dfrac{ 80 }{ 17 }\right)$ and $\left(4,~1\right)$. | 1 |
6288 | Find the sum of the vectors $ \vec{v_1} = \left(7,~1,~0\right) $ and $ \vec{v_2} = \left(1,~6,~7\right) $ . | 1 |
6289 | Determine whether the vectors $ \vec{v_1} = \left(89,~157\right) $ and $ \vec{v_2} = \left(237,~326\right) $ are linearly independent or dependent. | 1 |
6290 | Calculate the cross product of the vectors $ \vec{v_1} = \left(0,~0,~3\right) $ and $ \vec{v_2} = \left(7,~0,~0\right) $ . | 1 |
6291 | Find the projection of the vector $ \vec{v_1} = \left(3,~4,~-2\right) $ on the vector $ \vec{v_2} = \left(2,~-1,~2\right) $. | 1 |
6292 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-4,~3\right) $ . | 1 |
6293 | Find the projection of the vector $ \vec{v_1} = \left(1,~2\right) $ on the vector $ \vec{v_2} = \left(2,~0\right) $. | 1 |
6294 | Find the magnitude of the vector $ \| \vec{v} \| = \left(14,~2,~-2\right) $ . | 1 |
6295 | Find the magnitude of the vector $ \| \vec{v} \| = \left(5,~7\right) $ . | 1 |
6296 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-5,~1,~7\right) $ and $ \vec{v_2} = \left(3,~5,~9\right) $ . | 1 |
6297 | Determine whether the vectors $ \vec{v_1} = \left(-1,~2,~4\right) $, $ \vec{v_2} = \left(2,~1,~-2\right) $ and $ \vec{v_3} = \left(-3,~0,~5\right)$ are linearly independent or dependent. | 1 |
6298 | Calculate the dot product of the vectors $ \vec{v_1} = \left(\dfrac{ 1 }{ 8 },~\dfrac{ 7 }{ 8 }\right) $ and $ \vec{v_2} = \left(\dfrac{ 1 }{ 5 },~\dfrac{ 4 }{ 5 }\right) $ . | 1 |
6299 | Find the magnitude of the vector $ \| \vec{v} \| = \left(1,~-3\right) $ . | 1 |
6300 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-64,~-3,~33\right) $ and $ \vec{v_2} = \left(0,~-3,~2\right) $ . | 1 |