Vectors
(the database of solved problems)
All the problems and solutions shown below were generated using the Vectors Calculator.
| ID |
Problem |
Count |
| 5651 | Find the sum of the vectors $ \vec{v_1} = \left(\dfrac{ 5523 }{ 500 },~\dfrac{ 468877 }{ 100000 }\right) $ and $ \vec{v_2} = \left(-\dfrac{ 132849 }{ 10000 },~\dfrac{ 2229 }{ 250 }\right) $ . | 1 |
| 5652 | Find the magnitude of the vector $ \| \vec{v} \| = \left(\dfrac{ 5523 }{ 500 },~\dfrac{ 468877 }{ 100000 }\right) $ . | 1 |
| 5653 | Calculate the cross product of the vectors $ \vec{v_1} = \left(18,~27,~-12\right) $ and $ \vec{v_2} = \left(8,~8,~-6\right) $ . | 1 |
| 5654 | Find the magnitude of the vector $ \| \vec{v} \| = \left(\dfrac{ 69503 }{ 100000 },~0.0652,~\dfrac{ 30519 }{ 3125 }\right) $ . | 1 |
| 5655 | Find the projection of the vector $ \vec{v_1} = \left(\dfrac{ 69503 }{ 100000 },~0.0652,~\dfrac{ 30519 }{ 3125 }\right) $ on the vector $ \vec{v_2} = \left(0,~0,~\dfrac{ 49 }{ 5 }\right) $. | 1 |
| 5656 | 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 |
| 5657 | Find the sum of the vectors $ \vec{v_1} = \left(8,~8,~-4\right) $ and $ \vec{v_2} = \left(3,~-6,~9\right) $ . | 1 |
| 5658 | Find the difference of the vectors $ \vec{v_1} = \left(11,~2,~5\right) $ and $ \vec{v_2} = \left(8,~-4,~20\right) $ . | 1 |
| 5659 | Find the magnitude of the vector $ \| \vec{v} \| = \left(9,~2\right) $ . | 1 |
| 5660 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-1,~2\right) $ . | 1 |
| 5661 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~4,~-7\right) $ and $ \vec{v_2} = \left(2,~-1,~4\right) $ . | 1 |
| 5662 | Calculate the cross product of the vectors $ \vec{v_1} = \left(3,~-1,~-1\right) $ and $ \vec{v_2} = \left(-1,~2,~-1\right) $ . | 1 |
| 5663 | Calculate the cross product of the vectors $ \vec{v_1} = \left(3,~4,~5\right) $ and $ \vec{v_2} = \left(-1,~-1,~7\right) $ . | 1 |
| 5664 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~2,~-\dfrac{ 3 }{ 5 }\right) $ and $ \vec{v_2} = \left(-3,~\dfrac{ 6 }{ 5 },~1\right) $ . | 1 |
| 5665 | Find the difference of the vectors $ \vec{v_1} = \left(1,~-1\right) $ and $ \vec{v_2} = \left(-4,~-3\right) $ . | 1 |
| 5666 | Calculate the cross product of the vectors $ \vec{v_1} = \left(61,~-25,~8\right) $ and $ \vec{v_2} = \left(-6,~4,~-8\right) $ . | 1 |
| 5667 | Find the magnitude of the vector $ \| \vec{v} \| = \left(4,~2,~-12\right) $ . | 1 |
| 5668 | Find the angle between vectors $ \left(4,~2,~7\right)$ and $\left(-3,~1,~2\right)$. | 1 |
| 5669 | Find the angle between vectors $ \left(1,~4,~-2\right)$ and $\left(-3,~12,~6\right)$. | 1 |
| 5670 | Find the magnitude of the vector $ \| \vec{v} \| = \left(6,~-1,~0\right) $ . | 1 |
| 5671 | Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~4,~5\right) $ and $ \vec{v_2} = \left(2,~-3,~-4\right) $ . | 1 |
| 5672 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~-3\right) $ and $ \vec{v_2} = \left(-1,~-3\right) $ . | 1 |
| 5673 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-1,~-3\right) $ and $ \vec{v_2} = \left(-1,~-3\right) $ . | 1 |
| 5674 | Calculate the cross product of the vectors $ \vec{v_1} = \left(4,~2,~-2\right) $ and $ \vec{v_2} = \left(0,~1,~-3\right) $ . | 1 |
| 5675 | Calculate the cross product of the vectors $ \vec{v_1} = \left(4,~2,~-2\right) $ and $ \vec{v_2} = \left(1,~5,~5\right) $ . | 1 |
| 5676 | Calculate the cross product of the vectors $ \vec{v_1} = \left(2,~1,~-3\right) $ and $ \vec{v_2} = \left(0,~2,~-5\right) $ . | 1 |
| 5677 | Find the magnitude of the vector $ \| \vec{v} \| = \left(1,~2,~4\right) $ . | 1 |
| 5678 | Find the magnitude of the vector $ \| \vec{v} \| = \left(\dfrac{ 3 }{ 5 },~-\dfrac{ 3 }{ 5 },~-1\right) $ . | 1 |
| 5679 | Find the projection of the vector $ \vec{v_1} = \left(0,~-4\right) $ on the vector $ \vec{v_2} = \left(0,~\dfrac{ 1 }{ 2 }\right) $. | 1 |
| 5680 | Find the projection of the vector $ \vec{v_1} = \left(0,~-4\right) $ on the vector $ \vec{v_2} = \left(\dfrac{\sqrt{ 3 }}{ 2 },~\dfrac{ 1 }{ 2 }\right) $. | 1 |
| 5681 | Find the projection of the vector $ \vec{v_1} = \left(0,~-4\right) $ on the vector $ \vec{v_2} = \left(\dfrac{ 1 }{ 2 },~- \dfrac{\sqrt{ 3 }}{ 2 }\right) $. | 1 |
| 5682 | Calculate the cross product of the vectors $ \vec{v_1} = \left(4,~2,~-4\right) $ and $ \vec{v_2} = \left(0,~3,~-4\right) $ . | 1 |
| 5683 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-4,~-2,~4\right) $ and $ \vec{v_2} = \left(0,~3,~-4\right) $ . | 1 |
| 5684 | Find the sum of the vectors $ \vec{v_1} = \left(2,~4,~7\right) $ and $ \vec{v_2} = \left(0,~3,~-4\right) $ . | 1 |
| 5685 | Calculate the cross product of the vectors $ \vec{v_1} = \left(2,~7,~3\right) $ and $ \vec{v_2} = \left(4,~2,~-4\right) $ . | 1 |
| 5686 | Find the sum of the vectors $ \vec{v_1} = \left(0,~3,~-4\right) $ and $ \vec{v_2} = \left(2,~4,~7\right) $ . | 1 |
| 5687 | Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~-3,~5\right) $ and $ \vec{v_2} = \left(-2,~4,~-1\right) $ . | 1 |
| 5688 | Calculate the cross product of the vectors $ \vec{v_1} = \left(4,~2,~-4\right) $ and $ \vec{v_2} = \left(2,~7,~3\right) $ . | 1 |
| 5689 | Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~-3,~5\right) $ and $ \vec{v_2} = \left(-3,~-4,~-3\right) $ . | 1 |
| 5690 | Calculate the cross product of the vectors $ \vec{v_1} = \left(2,~4,~7\right) $ and $ \vec{v_2} = \left(0,~3,~-4\right) $ . | 1 |
| 5691 | Calculate the cross product of the vectors $ \vec{v_1} = \left(2,~4,~7\right) $ and $ \vec{v_2} = \left(-37,~8,~6\right) $ . | 1 |
| 5692 | Calculate the cross product of the vectors $ \vec{v_1} = \left(2,~4,~7\right) $ and $ \vec{v_2} = \left(2,~4,~7\right) $ . | 1 |
| 5693 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-3,~-4,~-3\right) $ and $ \vec{v_2} = \left(-3,~-4,~-3\right) $ . | 1 |
| 5694 | Calculate the dot product of the vectors $ \vec{v_1} = \left(102,~-102,~170\right) $ and $ \vec{v_2} = \left(3,~-3,~5\right) $ . | 1 |
| 5695 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-2,~4,~-1\right) $ and $ \vec{v_2} = \left(-3,~-4,~-3\right) $ . | 1 |
| 5696 | Find the angle between vectors $ \left(-5,~1,~0\right)$ and $\left(3,~8,~9\right)$. | 1 |
| 5697 | Find the projection of the vector $ \vec{v_1} = \left(1,~0,~3\right) $ on the vector $ \vec{v_2} = \left(1,~2,~-1\right) $. | 1 |
| 5698 | Find the magnitude of the vector $ \| \vec{v} \| = \left(3,~5\right) $ . | 1 |
| 5699 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-1,~-3,~-3\right) $ and $ \vec{v_2} = \left(1,~-5,~6\right) $ . | 1 |
| 5700 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-1,~-3,~-3\right) $ and $ \vec{v_2} = \left(1,~-5,~6\right) $ . | 1 |
