Vectors
(the database of solved problems)
All the problems and solutions shown below were generated using the Vectors Calculator.
| ID |
Problem |
Count |
| 2701 | Find the sum of the vectors $ \vec{v_1} = \left(2,~3,~-7\right) $ and $ \vec{v_2} = \left(-2,~-6,~8\right) $ . | 1 |
| 2702 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-2,~-1,~2\right) $ and $ \vec{v_2} = \left(1,~-1,~-4\right) $ . | 1 |
| 2703 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-2,~-1,~2\right) $ and $ \vec{v_2} = \left(4,~3,~-2\right) $ . | 1 |
| 2704 | 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 |
| 2705 | Calculate the dot product of the vectors $ \vec{v_1} = \left(\dfrac{ 1 }{ 10 },~\dfrac{ 22 }{ 5 }\right) $ and $ \vec{v_2} = \left(\dfrac{ 11 }{ 10 },~\dfrac{ 5 }{ 2 }\right) $ . | 1 |
| 2706 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-\dfrac{ 13 }{ 5 },~\dfrac{ 9 }{ 2 }\right) $ and $ \vec{v_2} = \left(\dfrac{ 11 }{ 10 },~\dfrac{ 5 }{ 2 }\right) $ . | 1 |
| 2707 | Determine whether the vectors $ \vec{v_1} = \left(2,~-2\right) $ and $ \vec{v_2} = \left(5,~-5\right) $ are linearly independent or dependent. | 1 |
| 2708 | Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~-2\right) $ and $ \vec{v_2} = \left(5,~-5\right) $ . | 1 |
| 2709 | Find the difference of the vectors $ \vec{v_1} = \left(6,~1\right) $ and $ \vec{v_2} = \left(\dfrac{ 26 }{ 5 },~\dfrac{ 13 }{ 5 }\right) $ . | 1 |
| 2710 | Find the projection of the vector $ \vec{v_1} = \left(-3,~1\right) $ on the vector $ \vec{v_2} = \left(8,~-6\right) $. | 1 |
| 2711 | Find the sum of the vectors $ \vec{v_1} = \left(0,~-40,~0\right) $ and $ \vec{v_2} = \left(40,~0,~-20\right) $ . | 1 |
| 2712 | Find the angle between vectors $ \left(0,~-40,~0\right)$ and $\left(40,~0,~-20\right)$. | 1 |
| 2713 | Find the magnitude of the vector $ \| \vec{v} \| = \left(4,~16\right) $ . | 1 |
| 2714 | Determine whether the vectors $ \vec{v_1} = \left(\dfrac{ 1 }{ 9 },~\dfrac{ 1 }{ 7 }\right) $ and $ \vec{v_2} = \left(\dfrac{ 8 }{ 9 },~\dfrac{ 6 }{ 7 }\right) $ are linearly independent or dependent. | 1 |
| 2715 | Find the projection of the vector $ \vec{v_1} = \left(\dfrac{ 1 }{ 9 },~\dfrac{ 1 }{ 7 }\right) $ on the vector $ \vec{v_2} = \left(\dfrac{ 8 }{ 9 },~\dfrac{ 6 }{ 7 }\right) $. | 1 |
| 2716 | Find the sum of the vectors $ \vec{v_1} = \left(-2,~2,~-3\right) $ and $ \vec{v_2} = \left(-1,~-1,~2\right) $ . | 1 |
| 2717 | Find the difference of the vectors $ \vec{v_1} = \left(-2,~2,~-3\right) $ and $ \vec{v_2} = \left(-1,~-1,~2\right) $ . | 1 |
| 2718 | Find the angle between vectors $ \left(1,~1\right)$ and $\left(-1,~0\right)$. | 1 |
| 2719 | Find the difference of the vectors $ \vec{v_1} = \left(-1,~-2\right) $ and $ \vec{v_2} = \left(0,~-2\right) $ . | 1 |
| 2720 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-1,~0\right) $ and $ \vec{v_2} = \left(0,~5\right) $ . | 1 |
| 2721 | Find the projection of the vector $ \vec{v_1} = \left(\dfrac{ 1 }{ 2 },~\dfrac{\sqrt{ 3 }}{ 2 }\right) $ on the vector $ \vec{v_2} = \left(- \dfrac{\sqrt{ 2 }}{ 2 },~\dfrac{\sqrt{ 2 }}{ 2 }\right) $. | 1 |
| 2722 | Find the magnitude of the vector $ \| \vec{v} \| = \left(0,~-40,~0\right) $ . | 1 |
| 2723 | Calculate the dot product of the vectors $ \vec{v_1} = \left(7,~-4,~1\right) $ and $ \vec{v_2} = \left(4,~-9,~2\right) $ . | 1 |
| 2724 | Calculate the dot product of the vectors $ \vec{v_1} = \left(5,~2,~-2\right) $ and $ \vec{v_2} = \left(2,~-1,~4\right) $ . | 1 |
| 2725 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-5,~8,~0\right) $ and $ \vec{v_2} = \left(4,~7,~-8\right) $ . | 1 |
| 2726 | Find the angle between vectors $ \left(-5,~8,~0\right)$ and $\left(4,~7,~-8\right)$. | 1 |
| 2727 | Find the angle between vectors $ \left(7,~-6\right)$ and $\left(2,~-9\right)$. | 1 |
| 2728 | Find the sum of the vectors $ \vec{v_1} = \left(182,~48\right) $ and $ \vec{v_2} = \left(48,~0\right) $ . | 1 |
| 2729 | Find the angle between vectors $ \left(5,~-2\right)$ and $\left(-6,~4\right)$. | 1 |
| 2730 | Find the difference of the vectors $ \vec{v_1} = \left(3,~5,~1\right) $ and $ \vec{v_2} = \left(-6,~5,~-2\right) $ . | 1 |
| 2731 | Find the sum of the vectors $ \vec{v_1} = \left(2,~1,~1\right) $ and $ \vec{v_2} = \left(-2,~2,~3\right) $ . | 1 |
| 2732 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-3,~0,~3\right) $ and $ \vec{v_2} = \left(-2,~3,~-2\right) $ . | 1 |
| 2733 | Find the angle between vectors $ \left(2,~1\right)$ and $\left(2,~3\right)$. | 1 |
| 2734 | Find the angle between vectors $ \left(2,~2\right)$ and $\left(1,~3\right)$. | 1 |
| 2735 | Find the magnitude of the vector $ \| \vec{v} \| = \left(3,~-6\right) $ . | 1 |
| 2736 | Find the projection of the vector $ \vec{v_1} = \left(11,~11 \sqrt{ 3 }\right) $ on the vector $ \vec{v_2} = \left(0,~0\right) $. | 1 |
| 2737 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-\sqrt{ 3 },~-1\right) $ and $ \vec{v_2} = \left(0,~\dfrac{ 3 }{ 2 }\right) $ . | 1 |
| 2738 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-\sqrt{ 3 },~-1\right) $ and $ \vec{v_2} = \left(- \dfrac{\sqrt{ 3 }}{ 2 },~\dfrac{ 3 }{ 2 }\right) $ . | 1 |
| 2739 | Find the projection of the vector $ \vec{v_1} = \left(-4,~4\right) $ on the vector $ \vec{v_2} = \left(-2,~4\right) $. | 1 |
| 2740 | Find the difference of the vectors $ \vec{v_1} = \left(-4,~4\right) $ and $ \vec{v_2} = \left(-\dfrac{ 12 }{ 5 },~\dfrac{ 24 }{ 5 }\right) $ . | 1 |
| 2741 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-2,~4\right) $ and $ \vec{v_2} = \left(-\dfrac{ 8 }{ 5 },~-\dfrac{ 4 }{ 5 }\right) $ . | 1 |
| 2742 | Find the magnitude of the vector $ \| \vec{v} \| = \left(2,~6\right) $ . | 1 |
| 2743 | Find the magnitude of the vector $ \| \vec{v} \| = \left(7,~2\right) $ . | 1 |
| 2744 | Calculate the cross product of the vectors $ \vec{v_1} = \left(2,~-1,~4\right) $ and $ \vec{v_2} = \left(1,~3,~7\right) $ . | 1 |
| 2745 | Find the sum of the vectors $ \vec{v_1} = \left(7,~-2\right) $ and $ \vec{v_2} = \left(-2,~-4\right) $ . | 1 |
| 2746 | Calculate the dot product of the vectors $ \vec{v_1} = \left(6,~1\right) $ and $ \vec{v_2} = \left(6,~1\right) $ . | 1 |
| 2747 | Find the angle between vectors $ \left(3,~0\right)$ and $\left(9,~2\right)$. | 1 |
| 2748 | Find the angle between vectors $ \left(0,~7,~-6\right)$ and $\left(2,~0,~-9\right)$. | 1 |
| 2749 | Find the magnitude of the vector $ \| \vec{v} \| = \left(1,~5,~3\right) $ . | 1 |
| 2750 | Find the sum of the vectors $ \vec{v_1} = \left(-2,~1\right) $ and $ \vec{v_2} = \left(2,~-2\right) $ . | 1 |
