Vectors
(the database of solved problems)
All the problems and solutions shown below were generated using the Vectors Calculator.
| ID |
Problem |
Count |
| 5351 | Find the magnitude of the vector $ \| \vec{v} \| = \left(4,~1\right) $ . | 1 |
| 5352 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-2,~-1,~1\right) $ and $ \vec{v_2} = \left(3,~-1,~-1\right) $ . | 1 |
| 5353 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-1,~1\right) $ . | 1 |
| 5354 | Find the difference of the vectors $ \vec{v_1} = \left(-1,~1\right) $ and $ \vec{v_2} = \left(4,~1\right) $ . | 1 |
| 5355 | Find the angle between vectors $ \left(5,~4\right)$ and $\left(6,~-1\right)$. | 1 |
| 5356 | Find the sum of the vectors $ \vec{v_1} = \left(3,~4\right) $ and $ \vec{v_2} = \left(1,~2\right) $ . | 1 |
| 5357 | Calculate the cross product of the vectors $ \vec{v_1} = \left(8,~-30,~-1\right) $ and $ \vec{v_2} = \left(4,~-12,~0\right) $ . | 1 |
| 5358 | Calculate the cross product of the vectors $ \vec{v_1} = \left(8,~-30,~-1\right) $ and $ \vec{v_2} = \left(-3,~-14,~-3\right) $ . | 1 |
| 5359 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~2,~-2\right) $ and $ \vec{v_2} = \left(3,~0,~1\right) $ . | 1 |
| 5360 | Calculate the cross product of the vectors $ \vec{v_1} = \left(8,~-30,~-1\right) $ and $ \vec{v_2} = \left(4,~-24,~0\right) $ . | 1 |
| 5361 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~2,~-2\right) $ and $ \vec{v_2} = \left(3,~0,~1\right) $ . | 1 |
| 5362 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~2,~-2\right) $ and $ \vec{v_2} = \left(2,~-7,~-6\right) $ . | 1 |
| 5363 | Find the difference of the vectors $ \vec{v_1} = \left(-2,~6\right) $ and $ \vec{v_2} = \left(-8,~-16\right) $ . | 1 |
| 5364 | Find the difference of the vectors $ \vec{v_1} = \left(-2,~6\right) $ and $ \vec{v_2} = \left(6,~-15\right) $ . | 1 |
| 5365 | Find the magnitude of the vector $ \| \vec{v} \| = \left(5,~-5\right) $ . | 1 |
| 5366 | Find the magnitude of the vector $ \| \vec{v} \| = \left(5,~5\right) $ . | 1 |
| 5367 | Find the magnitude of the vector $ \| \vec{v} \| = \left(1,~-3\right) $ . | 1 |
| 5368 | Find the magnitude of the vector $ \| \vec{v} \| = \left(2,~1\right) $ . | 1 |
| 5369 | Find the magnitude of the vector $ \| \vec{v} \| = \left(2,~13\right) $ . | 1 |
| 5370 | Find the magnitude of the vector $ \| \vec{v} \| = \left(2,~9\right) $ . | 1 |
| 5371 | Determine whether the vectors $ \vec{v_1} = \left(-\dfrac{ 4 }{ 3 },~\dfrac{ 5 }{ 2 }\right) $ and $ \vec{v_2} = \left(16,~-30\right) $ are linearly independent or dependent. | 1 |
| 5372 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-\dfrac{ 4 }{ 3 },~\dfrac{ 5 }{ 2 }\right) $ . | 1 |
| 5373 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~-1,~2\right) $ and $ \vec{v_2} = \left(-1,~1,~1\right) $ . | 1 |
| 5374 | Find the magnitude of the vector $ \| \vec{v} \| = \left(1,~-1,~2\right) $ . | 1 |
| 5375 | Find the sum of the vectors $ \vec{v_1} = \left(0,~5\right) $ and $ \vec{v_2} = \left(10,~0\right) $ . | 1 |
| 5376 | Find the magnitude of the vector $ \| \vec{v} \| = \left(10,~0\right) $ . | 1 |
| 5377 | Find the sum of the vectors $ \vec{v_1} = \left(7,~-1\right) $ and $ \vec{v_2} = \left(0,~6\right) $ . | 1 |
| 5378 | Find the angle between vectors $ \left(-1,~5\right)$ and $\left(6,~8\right)$. | 1 |
| 5379 | Find the sum of the vectors $ \vec{v_1} = \left(-1,~5\right) $ and $ \vec{v_2} = \left(6,~8\right) $ . | 1 |
| 5380 | Find the difference of the vectors $ \vec{v_1} = \left(-1,~5\right) $ and $ \vec{v_2} = \left(6,~8\right) $ . | 1 |
| 5381 | Find the magnitude of the vector $ \| \vec{v} \| = \left(2,~-3\right) $ . | 1 |
| 5382 | Find the magnitude of the vector $ \| \vec{v} \| = \left(8,~-2\right) $ . | 1 |
| 5383 | Find the magnitude of the vector $ \| \vec{v} \| = \left(8,~-2\right) $ . | 1 |
| 5384 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-8,~-6\right) $ . | 1 |
| 5385 | Find the magnitude of the vector $ \| \vec{v} \| = \left(10,~-8\right) $ . | 1 |
| 5386 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~-4,~0\right) $ and $ \vec{v_2} = \left(-3,~8,~0\right) $ . | 1 |
| 5387 | Determine whether the vectors $ \vec{v_1} = \left(0,~1,~2\right) $, $ \vec{v_2} = \left(0,~-2,~4\right) $ and $ \vec{v_3} = \left(0,~5,~2\right)$ are linearly independent or dependent. | 1 |
| 5388 | Determine whether the vectors $ \vec{v_1} = \left(2,~0,~2\right) $, $ \vec{v_2} = \left(1,~0,~-2\right) $ and $ \vec{v_3} = \left(2,~0,~1\right)$ are linearly independent or dependent. | 1 |
| 5389 | 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 |
| 5390 | Find the sum of the vectors $ \vec{v_1} = \left(-1,~7\right) $ and $ \vec{v_2} = \left(5,~-4\right) $ . | 1 |
| 5391 | Calculate the dot product of the vectors $ \vec{v_1} = \left(6,~8\right) $ and $ \vec{v_2} = \left(-4,~3\right) $ . | 1 |
| 5392 | Find the difference of the vectors $ \vec{v_1} = \left(6,~8\right) $ and $ \vec{v_2} = \left(-4,~3\right) $ . | 1 |
| 5393 | Find the projection of the vector $ \vec{v_1} = \left(4,~5,~6\right) $ on the vector $ \vec{v_2} = \left(1,~2,~3\right) $. | 1 |
| 5394 | Find the projection of the vector $ \vec{v_1} = \left(3,~3,~5\right) $ on the vector $ \vec{v_2} = \left(4,~1,~0\right) $. | 1 |
| 5395 | Find the magnitude of the vector $ \| \vec{v} \| = \left(1,~3,~1\right) $ . | 1 |
| 5396 | Find the sum of the vectors $ \vec{v_1} = \left(1,~3,~1\right) $ and $ \vec{v_2} = \left(3,~2,~-1\right) $ . | 1 |
| 5397 | Find the projection of the vector $ \vec{v_1} = \left(\dfrac{ 5 }{ 81 },~-\dfrac{ 100 }{ 81 },~-\dfrac{ 10 }{ 81 }\right) $ on the vector $ \vec{v_2} = \left(1,~-1,~-1\right) $. | 1 |
| 5398 | Find the projection of the vector $ \vec{v_1} = \left(4,~1,~-8\right) $ on the vector $ \vec{v_2} = \left(1,~-1,~-1\right) $. | 1 |
| 5399 | Find the projection of the vector $ \vec{v_1} = \left(4,~1,~-8\right) $ on the vector $ \vec{v_2} = \left(1,~-1,~-2\right) $. | 1 |
| 5400 | Find the projection of the vector $ \vec{v_1} = \left(1,~-1,~-2\right) $ on the vector $ \vec{v_2} = \left(4,~1,~-8\right) $. | 1 |
