Vectors
(the database of solved problems)
All the problems and solutions shown below were generated using the Vectors Calculator.
| ID |
Problem |
Count |
| 5701 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~1,~3\right) $ and $ \vec{v_2} = \left(2,~1,~2\right) $ . | 1 |
| 5702 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~1,~3\right) $ and $ \vec{v_2} = \left(2,~1,~2\right) $ . | 1 |
| 5703 | Calculate the dot product of the vectors $ \vec{v_1} = \left(0,~2,~0\right) $ and $ \vec{v_2} = \left(1,~1,~0\right) $ . | 1 |
| 5704 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~-5,~2\right) $ and $ \vec{v_2} = \left(3,~1,~-10\right) $ . | 1 |
| 5705 | Calculate the cross product of the vectors $ \vec{v_1} = \left(2,~7,~1\right) $ and $ \vec{v_2} = \left(0,~14,~2\right) $ . | 1 |
| 5706 | Find the projection of the vector $ \vec{v_1} = \left(-6,~-2,~6\right) $ on the vector $ \vec{v_2} = \left(-19,~-9,~16\right) $. | 1 |
| 5707 | Find the projection of the vector $ \vec{v_1} = \left(3,~5,~1\right) $ on the vector $ \vec{v_2} = \left(-2,~6,~-2\right) $. | 1 |
| 5708 | Determine whether the vectors $ \vec{v_1} = \left(1,~3,~0\right) $, $ \vec{v_2} = \left(-2,~0,~1\right) $ and $ \vec{v_3} = \left(0,~0,~0\right)$ are linearly independent or dependent. | 1 |
| 5709 | Determine whether the vectors $ \vec{v_1} = \left(1,~3,~0\right) $, $ \vec{v_2} = \left(-2,~0,~1\right) $ and $ \vec{v_3} = \left(-2,~\dfrac{ 7 }{ 2 },~7\right)$ are linearly independent or dependent. | 1 |
| 5710 | Find the magnitude of the vector $ \| \vec{v} \| = \left(2,~4\right) $ . | 1 |
| 5711 | Find the sum of the vectors $ \vec{v_1} = \left(2,~4\right) $ and $ \vec{v_2} = \left(5,~6\right) $ . | 1 |
| 5712 | Find the projection of the vector $ \vec{v_1} = \left(2,~4\right) $ on the vector $ \vec{v_2} = \left(5,~6\right) $. | 1 |
| 5713 | Find the difference of the vectors $ \vec{v_1} = \left(\dfrac{ 657 }{ 1000 },~\dfrac{ 13 }{ 500 },~\dfrac{ 377 }{ 500 }\right) $ and $ \vec{v_2} = \left(\dfrac{ 293 }{ 500 },~-\dfrac{ 807 }{ 1000 },~\dfrac{ 69 }{ 1000 }\right) $ . | 1 |
| 5714 | Determine whether the vectors $ \vec{v_1} = \left(1,~-2\right) $ and $ \vec{v_2} = \left(-4,~8\right) $ are linearly independent or dependent. | 1 |
| 5715 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~-2\right) $ and $ \vec{v_2} = \left(-4,~8\right) $ . | 1 |
| 5716 | Find the magnitude of the vector $ \| \vec{v} \| = \left(1,~-2\right) $ . | 1 |
| 5717 | Find the difference of the vectors $ \vec{v_1} = \left(0,~-7\right) $ and $ \vec{v_2} = \left(1,~-2\right) $ . | 1 |
| 5718 | Find the difference of the vectors $ \vec{v_1} = \left(0,~-21\right) $ and $ \vec{v_2} = \left(4,~-8\right) $ . | 1 |
| 5719 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-2,~5\right) $ . | 1 |
| 5720 | Find the sum of the vectors $ \vec{v_1} = \left(3,~-2\right) $ and $ \vec{v_2} = \left(5,~1\right) $ . | 1 |
| 5721 | Find the magnitude of the vector $ \| \vec{v} \| = \left(3,~-2\right) $ . | 1 |
| 5722 | Find the magnitude of the vector $ \| \vec{v} \| = \left(1,~25\right) $ . | 1 |
| 5723 | Find the angle between vectors $ \left(-1,~25\right)$ and $\left(41,~1\right)$. | 1 |
| 5724 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-1,~-12,~-11\right) $ and $ \vec{v_2} = \left(3,~-2,~-7\right) $ . | 1 |
| 5725 | Find the sum of the vectors $ \vec{v_1} = \left(75,~-75 \sqrt{ 3 }\right) $ and $ \vec{v_2} = \left(\dfrac{ 175 \sqrt{ 3}}{ 4 },~43.75\right) $ . | 1 |
| 5726 | Calculate the cross product of the vectors $ \vec{v_1} = \left(3,~0,~-4\right) $ and $ \vec{v_2} = \left(0,~1,~2\right) $ . | 1 |
| 5727 | Calculate the cross product of the vectors $ \vec{v_1} = \left(0,~2,~1\right) $ and $ \vec{v_2} = \left(1,~-1,~0\right) $ . | 1 |
| 5728 | Determine whether the vectors $ \vec{v_1} = \left(0,~2,~1\right) $, $ \vec{v_2} = \left(1,~-1,~0\right) $ and $ \vec{v_3} = \left(-2,~1,~3\right)$ are linearly independent or dependent. | 1 |
| 5729 | Find the magnitude of the vector $ \| \vec{v} \| = \left(2,~7\right) $ . | 1 |
| 5730 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-1,~-2,~5\right) $ and $ \vec{v_2} = \left(2,~-4,~0\right) $ . | 1 |
| 5731 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-1,~-2,~4\right) $ and $ \vec{v_2} = \left(-1,~1,~-2\right) $ . | 1 |
| 5732 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-1,~-4,~2\right) $ and $ \vec{v_2} = \left(2,~2,~1\right) $ . | 1 |
| 5733 | Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~3,~-2\right) $ and $ \vec{v_2} = \left(-8,~5,~6\right) $ . | 1 |
| 5734 | Find the sum of the vectors $ \vec{v_1} = \left(2,~0\right) $ and $ \vec{v_2} = \left(1,~4\right) $ . | 1 |
| 5735 | Find the sum of the vectors $ \vec{v_1} = \left(1,~4\right) $ and $ \vec{v_2} = \left(2,~7\right) $ . | 1 |
| 5736 | Find the sum of the vectors $ \vec{v_1} = \left(-3,~11\right) $ and $ \vec{v_2} = \left(4,~5\right) $ . | 1 |
| 5737 | Find the sum of the vectors $ \vec{v_1} = \left(-3,~-11\right) $ and $ \vec{v_2} = \left(4,~5\right) $ . | 1 |
| 5738 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-4,~-5,~-2\right) $ and $ \vec{v_2} = \left(4,~2,~8\right) $ . | 1 |
| 5739 | Find the sum of the vectors $ \vec{v_1} = \left(6,~-2,~-1\right) $ and $ \vec{v_2} = \left(3,~5,~3\right) $ . | 1 |
| 5740 | Calculate the dot product of the vectors $ \vec{v_1} = \left(6,~-2,~-1\right) $ and $ \vec{v_2} = \left(3,~5,~3\right) $ . | 1 |
| 5741 | Find the angle between vectors $ \left(1,~3,~7\right)$ and $\left(3,~7,~2\right)$. | 1 |
| 5742 | Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~-1,~5\right) $ and $ \vec{v_2} = \left(2,~4,~0\right) $ . | 1 |
| 5743 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-3,~-2,~2\right) $ . | 1 |
| 5744 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-4,~6,~-10\right) $ and $ \vec{v_2} = \left(-2,~3,~-5\right) $ . | 1 |
| 5745 | Find the magnitude of the vector $ \| \vec{v} \| = \left(0,~0,~0\right) $ . | 1 |
| 5746 | Find the magnitude of the vector $ \| \vec{v} \| = \left(3,~0\right) $ . | 1 |
| 5747 | 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 |
| 5748 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-3,~4,~-4\right) $ and $ \vec{v_2} = \left(6,~4,~-1\right) $ . | 1 |
| 5749 | Find the angle between vectors $ \left(-3,~4,~-4\right)$ and $\left(6,~4,~-1\right)$. | 1 |
| 5750 | Calculate the dot product of the vectors $ \vec{v_1} = \left(12,~-9,~6\right) $ and $ \vec{v_2} = \left(-8,~6,~-4\right) $ . | 1 |
