Vectors – Solved Problems Database
All the problems and solutions shown below were generated using the Vectors Calculator.
ID |
Problem |
Count |
5451 | Find the projection of the vector $ \vec{v_1} = \left(-1,~-5,~5\right) $ on the vector $ \vec{v_2} = \left(1,~-4,~4\right) $. | 1 |
5452 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~2,~3\right) $ and $ \vec{v_2} = \left(-3,~6,~-9\right) $ . | 1 |
5453 | Calculate the cross product of the vectors $ \vec{v_1} = \left(2,~-3,~1\right) $ and $ \vec{v_2} = \left(-1,~1,~0\right) $ . | 1 |
5454 | Find the angle between vectors $ \left(-1,~3,~2\right)$ and $\left(1,~-3,~-2\right)$. | 1 |
5455 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~2,~0\right) $ and $ \vec{v_2} = \left(-2,~1,~0\right) $ . | 1 |
5456 | Find the difference of the vectors $ \vec{v_1} = \left(3,~2\right) $ and $ \vec{v_2} = \left(4,~6\right) $ . | 1 |
5457 | Find the difference of the vectors $ \vec{v_1} = \left(3,~-6\right) $ and $ \vec{v_2} = \left(0,~-9\right) $ . | 1 |
5458 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-6,~4\right) $ . | 1 |
5459 | Find the difference of the vectors $ \vec{v_1} = \left(1,~1\right) $ and $ \vec{v_2} = \left(0,~1\right) $ . | 1 |
5460 | Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~-1,~1\right) $ and $ \vec{v_2} = \left(3,~-1,~1\right) $ . | 1 |
5461 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~1,~1\right) $ and $ \vec{v_2} = \left(3,~3,~-2\right) $ . | 1 |
5462 | Find the angle between vectors $ \left(3,~-8,~6\right)$ and $\left(-5,~4,~9\right)$. | 1 |
5463 | Determine whether the vectors $ \vec{v_1} = \left(1,~2,~-3\right) $, $ \vec{v_2} = \left(4,~-5,~6\right) $ and $ \vec{v_3} = \left(3,~2,~-1\right)$ are linearly independent or dependent. | 1 |
5464 | Find the sum of the vectors $ \vec{v_1} = \left(\dfrac{ 1 }{ 10 },~\dfrac{ 9 }{ 10 }\right) $ and $ \vec{v_2} = \left(\dfrac{ 4 }{ 5 },~\dfrac{ 1 }{ 5 }\right) $ . | 1 |
5465 | Find the angle between vectors $ \left(4,~-5\right)$ and $\left(1,~9\right)$. | 1 |
5466 | Find the projection of the vector $ \vec{v_1} = \left(-5,~5\right) $ on the vector $ \vec{v_2} = \left(-1,~5\right) $. | 1 |
5467 | Find the projection of the vector $ \vec{v_1} = \left(-6,~-5,~-4\right) $ on the vector $ \vec{v_2} = \left(6,~-6,~-4\right) $. | 1 |
5468 | Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~-3\right) $ and $ \vec{v_2} = \left(3,~-3\right) $ . | 1 |
5469 | Find the magnitude of the vector $ \| \vec{v} \| = \left(2,~2,~2\right) $ . | 1 |
5470 | Find the angle between vectors $ \left(\dfrac{ 11 }{ 5 },~\dfrac{ 94 }{ 25 }\right)$ and $\left(1,~\dfrac{ 11 }{ 5 }\right)$. | 1 |
5471 | Find the angle between vectors $ \left(1,~1\right)$ and $\left(0,~1\right)$. | 1 |
5472 | Determine whether the vectors $ \vec{v_1} = \left(3,~-4\right) $ and $ \vec{v_2} = \left(4,~11\right) $ are linearly independent or dependent. | 1 |
5473 | Find the angle between vectors $ \left(5,~3,~5\right)$ and $\left(1,~-3,~-2\right)$. | 1 |
5474 | Calculate the dot product of the vectors $ \vec{v_1} = \left(8,~8\right) $ and $ \vec{v_2} = \left(8,~8\right) $ . | 1 |
5475 | Calculate the cross product of the vectors $ \vec{v_1} = \left(\dfrac{ 21 }{ 5 },~\dfrac{ 37 }{ 10 },~\dfrac{ 6 }{ 5 }\right) $ and $ \vec{v_2} = \left(\dfrac{ 33 }{ 10 },~0,~0\right) $ . | 1 |
5476 | Calculate the cross product of the vectors $ \vec{v_1} = \left(4,~-2,~-4\right) $ and $ \vec{v_2} = \left(1,~6,~7\right) $ . | 1 |
5477 | Find the sum of the vectors $ \vec{v_1} = \left(-4,~2,~-4\right) $ and $ \vec{v_2} = \left(-2,~9,~-2\right) $ . | 1 |
5478 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-\dfrac{ 6321 }{ 5000 },~-0.0809,~-1\right) $ . | 1 |
5479 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~0,~1\right) $ and $ \vec{v_2} = \left(1,~1,~1\right) $ . | 1 |
5480 | Find the angle between vectors $ \left(-1,~6,~1\right)$ and $\left(1,~-5,~0\right)$. | 1 |
5481 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-2,~\dfrac{ 2 }{ 3 },~-3\right) $ and $ \vec{v_2} = \left(4,~0,~-\dfrac{ 1 }{ 2 }\right) $ . | 1 |
5482 | Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~1,~2\right) $ and $ \vec{v_2} = \left(3,~5,~4\right) $ . | 1 |
5483 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-6,~4\right) $ and $ \vec{v_2} = \left(-3,~2\right) $ . | 1 |
5484 | Find the angle between vectors $ \left(4,~-2,~6\right)$ and $\left(-2,~1,~-3\right)$. | 1 |
5485 | Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~6,~-2\right) $ and $ \vec{v_2} = \left(5,~1,~-4\right) $ . | 1 |
5486 | Find the magnitude of the vector $ \| \vec{v} \| = \left(1,~2,~2\right) $ . | 1 |
5487 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~-1,~2\right) $ and $ \vec{v_2} = \left(2,~3,~1\right) $ . | 1 |
5488 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~1,~-7\right) $ and $ \vec{v_2} = \left(2,~-1,~7\right) $ . | 1 |
5489 | Find the sum of the vectors $ \vec{v_1} = \left(4,~1\right) $ and $ \vec{v_2} = \left(-2,~3\right) $ . | 1 |
5490 | Find the magnitude of the vector $ \| \vec{v} \| = \left(3,~6\right) $ . | 1 |
5491 | Find the projection of the vector $ \vec{v_1} = \left(1,~5,~-1\right) $ on the vector $ \vec{v_2} = \left(2,~0,~4\right) $. | 1 |
5492 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-\dfrac{ 6321 }{ 5000 },~-0.0809,~-1\right) $ and $ \vec{v_2} = \left(0,~1,~0\right) $ . | 1 |
5493 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~0,~1\right) $ and $ \vec{v_2} = \left(1,~-1,~2\right) $ . | 1 |
5494 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~3,~-8\right) $ and $ \vec{v_2} = \left(4,~-5,~4\right) $ . | 1 |
5495 | Find the sum of the vectors $ \vec{v_1} = \left(0,~1,~-2\right) $ and $ \vec{v_2} = \left(1,~-4,~-2\right) $ . | 1 |
5496 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~0,~-1\right) $ and $ \vec{v_2} = \left(6,~8,~6\right) $ . | 1 |
5497 | Find the sum of the vectors $ \vec{v_1} = \left(1,~2,~0\right) $ and $ \vec{v_2} = \left(-2,~1,~0\right) $ . | 1 |
5498 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-2,~-3\right) $ and $ \vec{v_2} = \left(1,~5\right) $ . | 1 |
5499 | Find the difference of the vectors $ \vec{v_1} = \left(-9,~9\right) $ and $ \vec{v_2} = \left(-1,~-5\right) $ . | 1 |
5500 | Find the angle between vectors $ \left(-5,~2\right)$ and $\left(-3,~7\right)$. | 1 |