Vectors
(the database of solved problems)
All the problems and solutions shown below were generated using the Vectors Calculator.
| ID |
Problem |
Count |
| 4301 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-6,~7,~2\right) $ and $ \vec{v_2} = \left(8,~5,~-3\right) $ . | 1 |
| 4302 | Find the magnitude of the vector $ \| \vec{v} \| = \left(5,~7\right) $ . | 1 |
| 4303 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-6,~4,~-4\right) $ and $ \vec{v_2} = \left(2,~4,~-1\right) $ . | 1 |
| 4304 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-6,~4,~-4\right) $ and $ \vec{v_2} = \left(2,~4,~-1\right) $ . | 1 |
| 4305 | Calculate the cross product of the vectors $ \vec{v_1} = \left(12,~-9,~6\right) $ and $ \vec{v_2} = \left(-8,~6,~-4\right) $ . | 1 |
| 4306 | Calculate the dot product of the vectors $ \vec{v_1} = \left(12,~-9,~6\right) $ and $ \vec{v_2} = \left(-8,~6,~-4\right) $ . | 1 |
| 4307 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~1,~1\right) $ and $ \vec{v_2} = \left(1,~0,~-1\right) $ . | 1 |
| 4308 | Calculate the cross product of the vectors $ \vec{v_1} = \left(5,~5,~5\right) $ and $ \vec{v_2} = \left(5,~0,~-5\right) $ . | 1 |
| 4309 | Find the angle between vectors $ \left(-5,~5,~-6\right)$ and $\left(-2,~4,~0\right)$. | 1 |
| 4310 | Find the projection of the vector $ \vec{v_1} = \left(-5,~5,~-6\right) $ on the vector $ \vec{v_2} = \left(-2,~4,~0\right) $. | 1 |
| 4311 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-3,~-1\right) $ . | 1 |
| 4312 | Determine whether the vectors $ \vec{v_1} = \left(4,~-4,~8\right) $, $ \vec{v_2} = \left(5,~3,~26\right) $ and $ \vec{v_3} = \left(-4,~3,~-10\right)$ are linearly independent or dependent. | 1 |
| 4313 | Find the sum of the vectors $ \vec{v_1} = \left(-18,~6\right) $ and $ \vec{v_2} = \left(-1,~3\right) $ . | 1 |
| 4314 | Find the sum of the vectors $ \vec{v_1} = \left(18,~-6\right) $ and $ \vec{v_2} = \left(-1,~3\right) $ . | 1 |
| 4315 | Find the difference of the vectors $ \vec{v_1} = \left(-1,~3\right) $ and $ \vec{v_2} = \left(3,~-1\right) $ . | 1 |
| 4316 | Find the difference of the vectors $ \vec{v_1} = \left(-1,~3\right) $ and $ \vec{v_2} = \left(-3,~1\right) $ . | 1 |
| 4317 | Find the difference of the vectors $ \vec{v_1} = \left(-9,~3\right) $ and $ \vec{v_2} = \left(-3,~9\right) $ . | 1 |
| 4318 | Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~-3,~0\right) $ and $ \vec{v_2} = \left(-1,~2,~-4\right) $ . | 1 |
| 4319 | Calculate the cross product of the vectors $ \vec{v_1} = \left(2,~-3,~0\right) $ and $ \vec{v_2} = \left(-1,~2,~-4\right) $ . | 1 |
| 4320 | Find the difference of the vectors $ \vec{v_1} = \left(2,~-3,~0\right) $ and $ \vec{v_2} = \left(-1,~2,~-4\right) $ . | 1 |
| 4321 | Find the difference of the vectors $ \vec{v_1} = \left(4,~-6,~0\right) $ and $ \vec{v_2} = \left(-3,~6,~-12\right) $ . | 1 |
| 4322 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-1,~11,~0\right) $ . | 1 |
| 4323 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~-2 \sqrt{ 2 }\right) $ and $ \vec{v_2} = \left(1,~\sqrt{ 2 }\right) $ . | 1 |
| 4324 | Determine whether the vectors $ \vec{v_1} = \left(2,~-2\right) $ and $ \vec{v_2} = \left(-1,~3\right) $ are linearly independent or dependent. | 1 |
| 4325 | Find the magnitude of the vector $ \| \vec{v} \| = \left(5,~3\right) $ . | 1 |
| 4326 | Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~-1,~5\right) $ and $ \vec{v_2} = \left(6,~-7,~5\right) $ . | 1 |
| 4327 | Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~-1,~5\right) $ and $ \vec{v_2} = \left(6,~-7,~-5\right) $ . | 1 |
| 4328 | Find the projection of the vector $ \vec{v_1} = \left(2,~-1,~4\right) $ on the vector $ \vec{v_2} = \left(0,~1,~-3\right) $. | 1 |
| 4329 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~1,~0\right) $ and $ \vec{v_2} = \left(-2,~0,~1\right) $ . | 1 |
| 4330 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~2,~-1\right) $ and $ \vec{v_2} = \left(1,~-1,~2\right) $ . | 1 |
| 4331 | Find the angle between vectors $ \left(2,~3,~1\right)$ and $\left(4,~6,~2\right)$. | 1 |
| 4332 | Find the magnitude of the vector $ \| \vec{v} \| = \left(7,~7\right) $ . | 1 |
| 4333 | Find the angle between vectors $ \left(4,~2,~-5\right)$ and $\left(2,~-1,~3\right)$. | 1 |
| 4334 | Calculate the cross product of the vectors $ \vec{v_1} = \left(3,~-2,~0\right) $ and $ \vec{v_2} = \left(5,~-1,~7\right) $ . | 1 |
| 4335 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~1,~0\right) $ and $ \vec{v_2} = \left(0,~1,~1\right) $ . | 1 |
| 4336 | Find the magnitude of the vector $ \| \vec{v} \| = \left(3,~4\right) $ . | 1 |
| 4337 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-4,~3\right) $ . | 1 |
| 4338 | Find the angle between vectors $ \left(3,~4\right)$ and $\left(-4,~3\right)$. | 1 |
| 4339 | Find the angle between vectors $ \left(2,~3\right)$ and $\left(1,~0\right)$. | 1 |
| 4340 | Find the projection of the vector $ \vec{v_1} = \left(6,~9\right) $ on the vector $ \vec{v_2} = \left(\dfrac{ 465 }{ 74 },~\dfrac{ 651 }{ 74 }\right) $. | 1 |
| 4341 | Find the difference of the vectors $ \vec{v_1} = \left(6,~9\right) $ and $ \vec{v_2} = \left(\dfrac{ 465 }{ 74 },~\dfrac{ 651 }{ 74 }\right) $ . | 1 |
| 4342 | Find the angle between vectors $ \left(-4,~2,~-5\right)$ and $\left(0,~0,~3\right)$. | 1 |
| 4343 | Find the projection of the vector $ \vec{v_1} = \left(-4,~2,~-5\right) $ on the vector $ \vec{v_2} = \left(1,~1,~3\right) $. | 1 |
| 4344 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-4,~2,~-5\right) $ and $ \vec{v_2} = \left(1,~1,~3\right) $ . | 1 |
| 4345 | Determine whether the vectors $ \vec{v_1} = \left(-4,~2,~-5\right) $, $ \vec{v_2} = \left(1,~1,~3\right) $ and $ \vec{v_3} = \left(0,~0,~0\right)$ are linearly independent or dependent. | 1 |
| 4346 | Find the difference of the vectors $ \vec{v_1} = \left(-5,~3,~4\right) $ and $ \vec{v_2} = \left(1,~1,~2\right) $ . | 1 |
| 4347 | Determine whether the vectors $ \vec{v_1} = \left(-5,~3,~4\right) $, $ \vec{v_2} = \left(1,~1,~2\right) $ and $ \vec{v_3} = \left(0,~0,~0\right)$ are linearly independent or dependent. | 1 |
| 4348 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-5,~3,~4\right) $ and $ \vec{v_2} = \left(1,~1,~2\right) $ . | 1 |
| 4349 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-3,~2,~-5\right) $ . | 1 |
| 4350 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-3,~2,~-5\right) $ and $ \vec{v_2} = \left(1,~1,~4\right) $ . | 1 |
