Vectors – Solved Problems Database
All the problems and solutions shown below were generated using the Vectors Calculator.
ID |
Problem |
Count |
5601 | Find the difference of the vectors $ \vec{v_1} = \left(-1,~2,~8\right) $ and $ \vec{v_2} = \left(0,~0,~0\right) $ . | 1 |
5602 | Calculate the cross product of the vectors $ \vec{v_1} = \left(4,~-20,~12\right) $ and $ \vec{v_2} = \left(2,~4,~6\right) $ . | 1 |
5603 | Find the difference of the vectors $ \vec{v_1} = \left(-1,~5,~8\right) $ and $ \vec{v_2} = \left(2,~-7,~3\right) $ . | 1 |
5604 | Find the sum of the vectors $ \vec{v_1} = \left(2,~-1,~-3\right) $ and $ \vec{v_2} = \left(-4,~2,~3\right) $ . | 1 |
5605 | Find the angle between vectors $ \left(1,~-1,~0\right)$ and $\left(0,~-1,~1\right)$. | 1 |
5606 | Find the angle between vectors $ \left(-6,~0,~-3\right)$ and $\left(-6,~-\dfrac{ 9 }{ 2 },~0\right)$. | 1 |
5607 | Find the difference of the vectors $ \vec{v_1} = \left(0,~-21\right) $ and $ \vec{v_2} = \left(4,~-8\right) $ . | 1 |
5608 | Find the angle between vectors $ \left(1,~3,~7\right)$ and $\left(3,~7,~2\right)$. | 1 |
5609 | Find the difference of the vectors $ \vec{v_1} = \left(9,~-3\right) $ and $ \vec{v_2} = \left(-5,~2\right) $ . | 1 |
5610 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-8,~-4\right) $ and $ \vec{v_2} = \left(-8,~-5\right) $ . | 1 |
5611 | Find the projection of the vector $ \vec{v_1} = \left(1,~2,~-3\right) $ on the vector $ \vec{v_2} = \left(4,~-5,~6\right) $. | 1 |
5612 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~0,~1\right) $ and $ \vec{v_2} = \left(-1,~-1,~-1\right) $ . | 1 |
5613 | Find the sum of the vectors $ \vec{v_1} = \left(6,~-2\right) $ and $ \vec{v_2} = \left(-3,~8\right) $ . | 1 |
5614 | Find the magnitude of the vector $ \| \vec{v} \| = \left(4,~-2\right) $ . | 1 |
5615 | Calculate the cross product of the vectors $ \vec{v_1} = \left(3,~-3,~0\right) $ and $ \vec{v_2} = \left(-2,~2,~3\right) $ . | 1 |
5616 | Find the sum of the vectors $ \vec{v_1} = \left(-\dfrac{ 1 }{ 5 },~\dfrac{ 3 }{ 5 }\right) $ and $ \vec{v_2} = \left(1,~-\dfrac{ 1 }{ 5 }\right) $ . | 1 |
5617 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-10,~7\right) $ . | 1 |
5618 | Find the angle between vectors $ \left(3,~0,~-1\right)$ and $\left(-5,~0,~-2\right)$. | 1 |
5619 | Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~-6,~-1\right) $ and $ \vec{v_2} = \left(11,~5,~9\right) $ . | 1 |
5620 | Find the difference of the vectors $ \vec{v_1} = \left(4,~8\right) $ and $ \vec{v_2} = \left(10,~10\right) $ . | 1 |
5621 | Find the projection of the vector $ \vec{v_1} = \left(8,~1\right) $ on the vector $ \vec{v_2} = \left(-8,~4\right) $. | 1 |
5622 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-\dfrac{ 6879 }{ 5000 },~-0.192,~-1\right) $ and $ \vec{v_2} = \left(0,~1,~0\right) $ . | 1 |
5623 | Find the projection of the vector $ \vec{v_1} = \left(-2,~4\right) $ on the vector $ \vec{v_2} = \left(-2,~1\right) $. | 1 |
5624 | Find the angle between vectors $ \left(1,~3,~-8\right)$ and $\left(4,~-5,~4\right)$. | 1 |
5625 | Determine whether the vectors $ \vec{v_1} = \left(2,~-1,~0\right) $, $ \vec{v_2} = \left(0,~0,~2\right) $ and $ \vec{v_3} = \left(2,~0,~0\right)$ are linearly independent or dependent. | 1 |
5626 | Find the projection of the vector $ \vec{v_1} = \left(-2,~-1\right) $ on the vector $ \vec{v_2} = \left(1,~-6\right) $. | 1 |
5627 | Calculate the dot product of the vectors $ \vec{v_1} = \left(4,~0,~-3\right) $ and $ \vec{v_2} = \left(-1,~-7,~1\right) $ . | 1 |
5628 | Find the difference of the vectors $ \vec{v_1} = \left(-2,~1,~0\right) $ and $ \vec{v_2} = \left(1,~2,~0\right) $ . | 1 |
5629 | Find the sum of the vectors $ \vec{v_1} = \left(-4,~7\right) $ and $ \vec{v_2} = \left(5,~2\right) $ . | 1 |
5630 | Find the angle between vectors $ \left(4,~-2,~5\right)$ and $\left(5,~4,~-2\right)$. | 1 |
5631 | Find the angle between vectors $ \left(-6,~2,~3\right)$ and $\left(-6,~-\dfrac{ 9 }{ 2 },~0\right)$. | 1 |
5632 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~1,~1\right) $ and $ \vec{v_2} = \left(-2,~3,~5\right) $ . | 1 |
5633 | Calculate the cross product of the vectors $ \vec{v_1} = \left(3,~3,~4\right) $ and $ \vec{v_2} = \left(5,~3,~-6\right) $ . | 1 |
5634 | Find the magnitude of the vector $ \| \vec{v} \| = \left(6,~6,~6 \sqrt{ 2 }\right) $ . | 1 |
5635 | Find the angle between vectors $ \left(5,~3,~5\right)$ and $\left(-2,~1,~-1\right)$. | 1 |
5636 | Find the angle between vectors $ \left(1,~2\right)$ and $\left(6,~-1\right)$. | 1 |
5637 | Calculate the dot product of the vectors $ \vec{v_1} = \left(\dfrac{ 173 }{ 100 },~1\right) $ and $ \vec{v_2} = \left(-\dfrac{ 173 }{ 50 },~2\right) $ . | 1 |
5638 | Find the angle between vectors $ \left(4,~7\right)$ and $\left(8,~3\right)$. | 1 |
5639 | Find the angle between vectors $ \left(3,~0,~1\right)$ and $\left(6,~0,~2\right)$. | 1 |
5640 | Calculate the dot product of the vectors $ \vec{v_1} = \left(0,~-2,~1\right) $ and $ \vec{v_2} = \left(0,~3,~-3\right) $ . | 1 |
5641 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-5,~4,~12\right) $ and $ \vec{v_2} = \left(3,~4,~4\right) $ . | 1 |
5642 | Find the magnitude of the vector $ \| \vec{v} \| = \left(4,~-8\right) $ . | 1 |
5643 | Determine whether the vectors $ \vec{v_1} = \left(1,~8,~-1\right) $, $ \vec{v_2} = \left(6,~5,~2\right) $ and $ \vec{v_3} = \left(0,~0,~0\right)$ are linearly independent or dependent. | 1 |
5644 | Find the magnitude of the vector $ \| \vec{v} \| = \left(5,~2\right) $ . | 1 |
5645 | Find the magnitude of the vector $ \| \vec{v} \| = \left(2,~-6\right) $ . | 1 |
5646 | Find the sum of the vectors $ \vec{v_1} = \left(-4,~-6\right) $ and $ \vec{v_2} = \left(-1,~-2\right) $ . | 1 |
5647 | Find the angle between vectors $ \left(4,~-2,~5\right)$ and $\left(10,~0,~8\right)$. | 1 |
5648 | Find the magnitude of the vector $ \| \vec{v} \| = \left(4,~3,~5\right) $ . | 1 |
5649 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-6,~-4\right) $ and $ \vec{v_2} = \left(-9,~-5\right) $ . | 1 |
5650 | Find the difference of the vectors $ \vec{v_1} = \left(8,~-20\right) $ and $ \vec{v_2} = \left(0,~-16\right) $ . | 1 |