Vectors – Solved Problems Database
All the problems and solutions shown below were generated using the Vectors Calculator.
ID |
Problem |
Count |
6451 | 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 |
6452 | Find the magnitude of the vector $ \| \vec{v} \| = \left(0,~\dfrac{ 5919 }{ 20 }\right) $ . | 1 |
6453 | Find the angle between vectors $ \left(4,~0\right)$ and $\left(1,~8\right)$. | 1 |
6454 | Find the angle between vectors $ \left(2,~-10,~11\right)$ and $\left(3,~0,~-4\right)$. | 1 |
6455 | Find the difference of the vectors $ \vec{v_1} = \left(1,~1,~1\right) $ and $ \vec{v_2} = \left(2,~2,~0\right) $ . | 1 |
6456 | Find the magnitude of the vector $ \| \vec{v} \| = \left(8,~\dfrac{ 248 }{ 25 }\right) $ . | 1 |
6457 | Find the projection of the vector $ \vec{v_1} = \left(-4,~8\right) $ on the vector $ \vec{v_2} = \left(-5,~-2\right) $. | 1 |
6458 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-2,~2\right) $ and $ \vec{v_2} = \left(8,~-8\right) $ . | 1 |
6459 | Find the magnitude of the vector $ \| \vec{v} \| = \left(5318,~-1034,~-799\right) $ . | 1 |
6460 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-11,~18,~-11\right) $ and $ \vec{v_2} = \left(-9,~-10,~19\right) $ . | 1 |
6461 | Calculate the cross product of the vectors $ \vec{v_1} = \left(\dfrac{ 69503 }{ 100000 },~0.0652,~\dfrac{ 30519 }{ 3125 }\right) $ and $ \vec{v_2} = \left(0,~0,~\dfrac{ 49 }{ 5 }\right) $ . | 1 |
6462 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~-3\right) $ and $ \vec{v_2} = \left(-1,~-3\right) $ . | 1 |
6463 | Find the magnitude of the vector $ \| \vec{v} \| = \left(2,~1,~1\right) $ . | 1 |
6464 | Find the magnitude of the vector $ \| \vec{v} \| = \left(0,~0,~0\right) $ . | 1 |
6465 | Find the sum of the vectors $ \vec{v_1} = \left(2,~-4\right) $ and $ \vec{v_2} = \left(7,~-5\right) $ . | 1 |
6466 | Calculate the cross product of the vectors $ \vec{v_1} = \left(6,~3,~1\right) $ and $ \vec{v_2} = \left(4,~5,~2\right) $ . | 1 |
6467 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~-1,~2\right) $ and $ \vec{v_2} = \left(0,~1,~1\right) $ . | 1 |
6468 | Calculate the cross product of the vectors $ \vec{v_1} = \left(0,~1,~0\right) $ and $ \vec{v_2} = \left(1,~0,~0\right) $ . | 1 |
6469 | Find the angle between vectors $ \left(0,~\dfrac{ 5919 }{ 20 }\right)$ and $\left(0,~-\dfrac{ 147 }{ 20 }\right)$. | 1 |
6470 | Calculate the dot product of the vectors $ \vec{v_1} = \left(7,~-9\right) $ and $ \vec{v_2} = \left(-7,~3\right) $ . | 1 |
6471 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-\dfrac{ 3 }{ 5 },~\dfrac{ 4 }{ 5 }\right) $ . | 1 |
6472 | Find the magnitude of the vector $ \| \vec{v} \| = \left(2,~-7\right) $ . | 1 |
6473 | Find the magnitude of the vector $ \| \vec{v} \| = \left(4,~-3,~0\right) $ . | 1 |
6474 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-11,~18,~-11\right) $ and $ \vec{v_2} = \left(-9,~-10,~19\right) $ . | 1 |
6475 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-1,~-3\right) $ and $ \vec{v_2} = \left(-1,~-3\right) $ . | 1 |
6476 | Find the sum of the vectors $ \vec{v_1} = \left(1,~4\right) $ and $ \vec{v_2} = \left(2,~7\right) $ . | 1 |
6477 | Calculate the dot product of the vectors $ \vec{v_1} = \left(9,~-4\right) $ and $ \vec{v_2} = \left(7,~6\right) $ . | 1 |
6478 | Calculate the cross product of the vectors $ \vec{v_1} = \left(2,~1,~1\right) $ and $ \vec{v_2} = \left(3,~-1,~2\right) $ . | 1 |
6479 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-2,~5,~5\right) $ and $ \vec{v_2} = \left(-4,~-7,~3\right) $ . | 1 |
6480 | Find the sum of the vectors $ \vec{v_1} = \left(5,~0\right) $ and $ \vec{v_2} = \left(4.3493,~4.8304\right) $ . | 1 |
6481 | Calculate the cross product of the vectors $ \vec{v_1} = \left(0,~0,~-1\right) $ and $ \vec{v_2} = \left(-1,~0,~0\right) $ . | 1 |
6482 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~-3,~2\right) $ and $ \vec{v_2} = \left(-4,~2,~4\right) $ . | 1 |
6483 | Calculate the dot product of the vectors $ \vec{v_1} = \left(0,~-3,~-2\right) $ and $ \vec{v_2} = \left(0,~-1,~-1\right) $ . | 1 |
6484 | Find the difference of the vectors $ \vec{v_1} = \left(-1,~3\right) $ and $ \vec{v_2} = \left(3,~-1\right) $ . | 1 |
6485 | Find the sum of the vectors $ \vec{v_1} = \left(\dfrac{ 51 }{ 5 },~0\right) $ and $ \vec{v_2} = \left(\dfrac{ 23 }{ 2 },~33\right) $ . | 1 |
6486 | Find the magnitude of the vector $ \| \vec{v} \| = \left(8,~15\right) $ . | 1 |
6487 | Find the magnitude of the vector $ \| \vec{v} \| = \left(1,~1,~1\right) $ . | 1 |
6488 | Find the projection of the vector $ \vec{v_1} = \left(-3,~-5,~-1\right) $ on the vector $ \vec{v_2} = \left(-9,~4,~1\right) $. | 1 |
6489 | Find the angle between vectors $ \left(1,~2,~2\right)$ and $\left(2,~-4,~4\right)$. | 1 |
6490 | Calculate the cross product of the vectors $ \vec{v_1} = \left(0,~3,~-5\right) $ and $ \vec{v_2} = \left(2,~4,~0\right) $ . | 1 |
6491 | Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~1,~-2\right) $ and $ \vec{v_2} = \left(-2,~3,~6\right) $ . | 1 |
6492 | Find the angle between vectors $ \left(2,~-9\right)$ and $\left(-5,~5\right)$. | 1 |
6493 | Find the sum of the vectors $ \vec{v_1} = \left(-5,~3\right) $ and $ \vec{v_2} = \left(-6,~8\right) $ . | 1 |
6494 | Find the angle between vectors $ \left(1,~-2\right)$ and $\left(3,~1\right)$. | 1 |
6495 | Find the magnitude of the vector $ \| \vec{v} \| = \left(1,~1\right) $ . | 1 |
6496 | Find the difference of the vectors $ \vec{v_1} = \left(-1,~-9\right) $ and $ \vec{v_2} = \left(6,~-5\right) $ . | 1 |
6497 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~2,~3\right) $ and $ \vec{v_2} = \left(0,~0,~0\right) $ . | 1 |
6498 | Find the sum of the vectors $ \vec{v_1} = \left(2,~3,~1\right) $ and $ \vec{v_2} = \left(1,~3,~0\right) $ . | 1 |
6499 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-2,~4,~5\right) $ and $ \vec{v_2} = \left(-4,~-7,~3\right) $ . | 1 |
6500 | Determine whether the vectors $ \vec{v_1} = \left(2,~-2,~4\right) $, $ \vec{v_2} = \left(-1,~2,~3\right) $ and $ \vec{v_3} = \left(3,~2,~5\right)$ are linearly independent or dependent. | 1 |