Vectors
(the database of solved problems)
All the problems and solutions shown below were generated using the Vectors Calculator.
| ID |
Problem |
Count |
| 4701 | Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~0,~2\right) $ and $ \vec{v_2} = \left(2,~2 \sqrt{ 2 },~2\right) $ . | 1 |
| 4702 | Find the magnitude of the vector $ \| \vec{v} \| = \left(2,~0,~2\right) $ . | 1 |
| 4703 | Find the magnitude of the vector $ \| \vec{v} \| = \left(2,~2 \sqrt{ 2 },~2\right) $ . | 1 |
| 4704 | Calculate the cross product of the vectors $ \vec{v_1} = \left(2,~-1,~-2\right) $ and $ \vec{v_2} = \left(1,~2,~-3\right) $ . | 1 |
| 4705 | Find the difference of the vectors $ \vec{v_1} = \left(1,~3,~5\right) $ and $ \vec{v_2} = \left(-2,~-6,~1\right) $ . | 1 |
| 4706 | Find the difference of the vectors $ \vec{v_1} = \left(4,~10,~16\right) $ and $ \vec{v_2} = \left(-2,~-6,~1\right) $ . | 1 |
| 4707 | Calculate the cross product of the vectors $ \vec{v_1} = \left(3,~9,~4\right) $ and $ \vec{v_2} = \left(6,~16,~15\right) $ . | 1 |
| 4708 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~0,~-2\right) $ and $ \vec{v_2} = \left(0,~-1,~-2\right) $ . | 1 |
| 4709 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~0,~3\right) $ and $ \vec{v_2} = \left(0,~1,~2\right) $ . | 1 |
| 4710 | Find the difference of the vectors $ \vec{v_1} = \left(-2,~1,~4\right) $ and $ \vec{v_2} = \left(4,~-3,~5\right) $ . | 1 |
| 4711 | Find the difference of the vectors $ \vec{v_1} = \left(4,~-5,~-3\right) $ and $ \vec{v_2} = \left(4,~-3,~5\right) $ . | 1 |
| 4712 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-6,~4,~-1\right) $ and $ \vec{v_2} = \left(0,~-2,~-8\right) $ . | 1 |
| 4713 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-34,~-48,~12\right) $ and $ \vec{v_2} = \left(4,~-3,~5\right) $ . | 1 |
| 4714 | Calculate the dot product of the vectors $ \vec{v_1} = \left(4,~4,~2\right) $ and $ \vec{v_2} = \left(-2,~-2,~8\right) $ . | 1 |
| 4715 | Calculate the cross product of the vectors $ \vec{v_1} = \left(0,~7,~0\right) $ and $ \vec{v_2} = \left(\dfrac{ 62619 }{ 200 },~-\dfrac{ 52689 }{ 50 },~\dfrac{ 477603 }{ 1000 }\right) $ . | 1 |
| 4716 | Calculate the cross product of the vectors $ \vec{v_1} = \left(0,~7,~0\right) $ and $ \vec{v_2} = \left(313,~-1054,~478\right) $ . | 1 |
| 4717 | Calculate the cross product of the vectors $ \vec{v_1} = \left(0,~0.11,~0.6\right) $ and $ \vec{v_2} = \left(23,~47,~-47\right) $ . | 1 |
| 4718 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-2,~-7\right) $ and $ \vec{v_2} = \left(5,~-9\right) $ . | 1 |
| 4719 | Find the projection of the vector $ \vec{v_1} = \left(-2,~-7\right) $ on the vector $ \vec{v_2} = \left(5,~-9\right) $. | 1 |
| 4720 | Determine whether the vectors $ \vec{v_1} = \left(-2,~-7\right) $ and $ \vec{v_2} = \left(5,~-9\right) $ are linearly independent or dependent. | 1 |
| 4721 | Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~-1,~2\right) $ and $ \vec{v_2} = \left(1,~-1,~-2\right) $ . | 1 |
| 4722 | Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~-2,~-8\right) $ and $ \vec{v_2} = \left(-12,~8,~25\right) $ . | 1 |
| 4723 | Find the magnitude of the vector $ \| \vec{v} \| = \left(1,~3,~-1\right) $ . | 1 |
| 4724 | Find the difference of the vectors $ \vec{v_1} = \left(6,~8,~4\right) $ and $ \vec{v_2} = \left(8,~5,~7\right) $ . | 1 |
| 4725 | Find the difference of the vectors $ \vec{v_1} = \left(0,~8,~4\right) $ and $ \vec{v_2} = \left(5,~8,~5\right) $ . | 1 |
| 4726 | Find the magnitude of the vector $ \| \vec{v} \| = \left(200,~0\right) $ . | 1 |
| 4727 | Find the difference of the vectors $ \vec{v_1} = \left(200,~200\right) $ and $ \vec{v_2} = \left(200,~0\right) $ . | 1 |
| 4728 | Find the sum of the vectors $ \vec{v_1} = \left(5,~-20\right) $ and $ \vec{v_2} = \left(0,~-6\right) $ . | 1 |
| 4729 | Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~2,~1\right) $ and $ \vec{v_2} = \left(3,~2,~1\right) $ . | 1 |
| 4730 | Find the sum of the vectors $ \vec{v_1} = \left(12,~-15\right) $ and $ \vec{v_2} = \left(15,~5\right) $ . | 1 |
| 4731 | Find the magnitude of the vector $ \| \vec{v} \| = \left(3,~-3 \sqrt{ 3 }\right) $ . | 1 |
| 4732 | Find the difference of the vectors $ \vec{v_1} = \left(0,~2,~-5\right) $ and $ \vec{v_2} = \left(5,~-4,~4\right) $ . | 1 |
| 4733 | Calculate the dot product of the vectors $ \vec{v_1} = \left(0,~2,~-5\right) $ and $ \vec{v_2} = \left(5,~-4,~4\right) $ . | 1 |
| 4734 | Find the magnitude of the vector $ \| \vec{v} \| = \left(9,~5\right) $ . | 1 |
| 4735 | Determine whether the vectors $ \vec{v_1} = \left(9,~5\right) $ and $ \vec{v_2} = \left(\dfrac{ 3 }{ 2 },~\dfrac{ 5 }{ 6 }\right) $ are linearly independent or dependent. | 1 |
| 4736 | Find the magnitude of the vector $ \| \vec{v} \| = \left(0,~1,~-3\right) $ . | 1 |
| 4737 | Find the magnitude of the vector $ \| \vec{v} \| = \left(4,~3,~1\right) $ . | 1 |
| 4738 | Determine whether the vectors $ \vec{v_1} = \left(4,~3,~1\right) $, $ \vec{v_2} = \left(0,~0,~0\right) $ and $ \vec{v_3} = \left(0,~0,~0\right)$ are linearly independent or dependent. | 1 |
| 4739 | Calculate the cross product of the vectors $ \vec{v_1} = \left(4,~3,~1\right) $ and $ \vec{v_2} = \left(0,~0,~0\right) $ . | 1 |
| 4740 | Find the sum of the vectors $ \vec{v_1} = \left(-1,~5,~1\right) $ and $ \vec{v_2} = \left(-4,~-1,~-2\right) $ . | 1 |
| 4741 | Calculate the dot product of the vectors $ \vec{v_1} = \left(4,~4,~2\right) $ and $ \vec{v_2} = \left(-2,~-3,~10\right) $ . | 1 |
| 4742 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~0,~1\right) $ and $ \vec{v_2} = \left(0,~2,~3\right) $ . | 1 |
| 4743 | Find the difference of the vectors $ \vec{v_1} = \left(1,~5,~9\right) $ and $ \vec{v_2} = \left(-3,~-7,~1\right) $ . | 1 |
| 4744 | Find the difference of the vectors $ \vec{v_1} = \left(3,~11,~13\right) $ and $ \vec{v_2} = \left(-3,~-7,~1\right) $ . | 1 |
| 4745 | Calculate the cross product of the vectors $ \vec{v_1} = \left(4,~12,~8\right) $ and $ \vec{v_2} = \left(6,~18,~12\right) $ . | 1 |
| 4746 | Calculate the cross product of the vectors $ \vec{v_1} = \left(0,~5,~5\right) $ and $ \vec{v_2} = \left(5 \sqrt{ 2 },~5,~5\right) $ . | 1 |
| 4747 | Calculate the dot product of the vectors $ \vec{v_1} = \left(0,~5,~5\right) $ and $ \vec{v_2} = \left(5 \sqrt{ 2 },~5,~5\right) $ . | 1 |
| 4748 | Find the magnitude of the vector $ \| \vec{v} \| = \left(0,~5,~5\right) $ . | 1 |
| 4749 | Find the magnitude of the vector $ \| \vec{v} \| = \left(5 \sqrt{ 2 },~5,~5\right) $ . | 1 |
| 4750 | Find the sum of the vectors $ \vec{v_1} = \left(9,~3,~15 \sqrt{ 3 }\right) $ and $ \vec{v_2} = \left(12,~0,~36 \sqrt{ 3 }\right) $ . | 1 |
