Vectors
(the database of solved problems)
All the problems and solutions shown below were generated using the Vectors Calculator.
| ID |
Problem |
Count |
| 4601 | Calculate the cross product of the vectors $ \vec{v_1} = \left(9,~-3,~3\right) $ and $ \vec{v_2} = \left(-3,~1,~-1\right) $ . | 1 |
| 4602 | Find the magnitude of the vector $ \| \vec{v} \| = \left(2000,~0,~0\right) $ . | 1 |
| 4603 | Find the projection of the vector $ \vec{v_1} = \left(-3,~9\right) $ on the vector $ \vec{v_2} = \left(1,~2\right) $. | 1 |
| 4604 | Determine whether the vectors $ \vec{v_1} = \left(1,~-1,~0\right) $, $ \vec{v_2} = \left(2,~1,~-1\right) $ and $ \vec{v_3} = \left(-1,~1,~2\right)$ are linearly independent or dependent. | 1 |
| 4605 | 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 |
| 4606 | Calculate the cross product of the vectors $ \vec{v_1} = \left(\dfrac{ 33 }{ 10 },~0,~0\right) $ and $ \vec{v_2} = \left(\dfrac{ 21 }{ 5 },~\dfrac{ 37 }{ 10 },~\dfrac{ 6 }{ 5 }\right) $ . | 1 |
| 4607 | Find the magnitude of the vector $ \| \vec{v} \| = \left(2,~-2,~4\right) $ . | 1 |
| 4608 | Find the magnitude of the vector $ \| \vec{v} \| = \left(4,~0,~3\right) $ . | 1 |
| 4609 | Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~-2,~1\right) $ and $ \vec{v_2} = \left(4,~0,~3\right) $ . | 1 |
| 4610 | Calculate the cross product of the vectors $ \vec{v_1} = \left(2,~-2,~1\right) $ and $ \vec{v_2} = \left(4,~0,~3\right) $ . | 1 |
| 4611 | Find the angle between vectors $ \left(2,~-2,~1\right)$ and $\left(4,~0,~3\right)$. | 1 |
| 4612 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-1,~-1\right) $ and $ \vec{v_2} = \left(-2,~-2\right) $ . | 1 |
| 4613 | Find the sum of the vectors $ \vec{v_1} = \left(40,~80\right) $ and $ \vec{v_2} = \left(50,~100\right) $ . | 1 |
| 4614 | Find the difference of the vectors $ \vec{v_1} = \left(6,~-4\right) $ and $ \vec{v_2} = \left(1,~8\right) $ . | 1 |
| 4615 | Find the difference of the vectors $ \vec{v_1} = \left(4,~2\right) $ and $ \vec{v_2} = \left(6,~-4\right) $ . | 1 |
| 4616 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-2,~6\right) $ . | 1 |
| 4617 | Find the magnitude of the vector $ \| \vec{v} \| = \left(5,~-12\right) $ . | 1 |
| 4618 | Find the sum of the vectors $ \vec{v_1} = \left(12,~6,~8 \sqrt{ 5 }\right) $ and $ \vec{v_2} = \left(12,~0,~20 \sqrt{ 5 }\right) $ . | 1 |
| 4619 | Find the difference of the vectors $ \vec{v_1} = \left(24,~12,~16 \sqrt{ 5 }\right) $ and $ \vec{v_2} = \left(3,~0,~5 \sqrt{ 5 }\right) $ . | 1 |
| 4620 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-5,~5\right) $ and $ \vec{v_2} = \left(-2,~1\right) $ . | 1 |
| 4621 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-2,~1\right) $ . | 1 |
| 4622 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~5,~4\right) $ and $ \vec{v_2} = \left(6,~-2,~1\right) $ . | 1 |
| 4623 | 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 |
| 4624 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~6,~7\right) $ and $ \vec{v_2} = \left(1,~-1,~-2\right) $ . | 1 |
| 4625 | Find the sum of the vectors $ \vec{v_1} = \left(2,~3,~4\right) $ and $ \vec{v_2} = \left(4,~5,~3\right) $ . | 1 |
| 4626 | Find the sum of the vectors $ \vec{v_1} = \left(10,~-5\right) $ and $ \vec{v_2} = \left(2,~-2\right) $ . | 1 |
| 4627 | Find the magnitude of the vector $ \| \vec{v} \| = \left(5,~5 \sqrt{ 2 },~5\right) $ . | 1 |
| 4628 | Find the magnitude of the vector $ \| \vec{v} \| = \left(3,~4,~-8\right) $ . | 1 |
| 4629 | Calculate the cross product of the vectors $ \vec{v_1} = \left(3,~4,~-8\right) $ and $ \vec{v_2} = \left(1,~1,~-1\right) $ . | 1 |
| 4630 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~1,~-1\right) $ and $ \vec{v_2} = \left(3,~4,~-8\right) $ . | 1 |
| 4631 | Calculate the cross product of the vectors $ \vec{v_1} = \left(5,~6,~7\right) $ and $ \vec{v_2} = \left(10,~12,~14\right) $ . | 1 |
| 4632 | Calculate the cross product of the vectors $ \vec{v_1} = \left(2,~0,~2\right) $ and $ \vec{v_2} = \left(0,~-2,~-1\right) $ . | 1 |
| 4633 | Calculate the cross product of the vectors $ \vec{v_1} = \left(2,~0,~3\right) $ and $ \vec{v_2} = \left(0,~2,~1\right) $ . | 1 |
| 4634 | Find the difference of the vectors $ \vec{v_1} = \left(4,~4,~5\right) $ and $ \vec{v_2} = \left(0,~-5,~3\right) $ . | 1 |
| 4635 | Find the difference of the vectors $ \vec{v_1} = \left(0,~-2,~1\right) $ and $ \vec{v_2} = \left(0,~-5,~3\right) $ . | 1 |
| 4636 | Calculate the cross product of the vectors $ \vec{v_1} = \left(4,~9,~2\right) $ and $ \vec{v_2} = \left(0,~3,~-2\right) $ . | 1 |
| 4637 | Calculate the dot product of the vectors $ \vec{v_1} = \left(4,~2,~2\right) $ and $ \vec{v_2} = \left(-3,~-4,~10\right) $ . | 1 |
| 4638 | Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~2,~-3\right) $ and $ \vec{v_2} = \left(-6,~-10,~1\right) $ . | 1 |
| 4639 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~-1,~-3\right) $ and $ \vec{v_2} = \left(4,~-3,~-1\right) $ . | 1 |
| 4640 | Calculate the cross product of the vectors $ \vec{v_1} = \left(3,~1,~2\right) $ and $ \vec{v_2} = \left(2,~-2,~4\right) $ . | 1 |
| 4641 | Calculate the cross product of the vectors $ \vec{v_1} = \left(2,~1,~1\right) $ and $ \vec{v_2} = \left(1,~-1,~2\right) $ . | 1 |
| 4642 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~-1,~4\right) $ and $ \vec{v_2} = \left(2,~-3,~0\right) $ . | 1 |
| 4643 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~-1,~4\right) $ and $ \vec{v_2} = \left(2,~0,~-3\right) $ . | 1 |
| 4644 | Calculate the cross product of the vectors $ \vec{v_1} = \left(4,~-2,~-4\right) $ and $ \vec{v_2} = \left(1,~-1,~-2\right) $ . | 1 |
| 4645 | Calculate the cross product of the vectors $ \vec{v_1} = \left(2,~3,~7\right) $ and $ \vec{v_2} = \left(3,~-2,~-3\right) $ . | 1 |
| 4646 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~1\right) $ and $ \vec{v_2} = \left(-1,~1\right) $ . | 1 |
| 4647 | 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 |
| 4648 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-3,~-1,~1\right) $ and $ \vec{v_2} = \left(2,~0,~3\right) $ . | 1 |
| 4649 | Calculate the cross product of the vectors $ \vec{v_1} = \left(0,~1,~1\right) $ and $ \vec{v_2} = \left(2,~0,~3\right) $ . | 1 |
| 4650 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~-1,~2\right) $ and $ \vec{v_2} = \left(3,~2,~-2\right) $ . | 1 |
