Vectors
(the database of solved problems)
All the problems and solutions shown below were generated using the Vectors Calculator.
| ID |
Problem |
Count |
| 2751 | Find the sum of the vectors $ \vec{v_1} = \left(2,~5\right) $ and $ \vec{v_2} = \left(-4,~1\right) $ . | 1 |
| 2752 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~-4,~1\right) $ and $ \vec{v_2} = \left(0,~8,~-8\right) $ . | 1 |
| 2753 | Find the sum of the vectors $ \vec{v_1} = \left(5,~1\right) $ and $ \vec{v_2} = \left(5,~-1\right) $ . | 1 |
| 2754 | Find the difference of the vectors $ \vec{v_1} = \left(5,~1\right) $ and $ \vec{v_2} = \left(5,~-1\right) $ . | 1 |
| 2755 | Find the sum of the vectors $ \vec{v_1} = \left(-7,~9\right) $ and $ \vec{v_2} = \left(14,~-12\right) $ . | 1 |
| 2756 | Find the magnitude of the vector $ \| \vec{v} \| = \left(9,~30\right) $ . | 1 |
| 2757 | Calculate the dot product of the vectors $ \vec{v_1} = \left(6,~3\right) $ and $ \vec{v_2} = \left(-6,~12\right) $ . | 1 |
| 2758 | Find the projection of the vector $ \vec{v_1} = \left(3,~-1,~1\right) $ on the vector $ \vec{v_2} = \left(6,~7,~-6\right) $. | 1 |
| 2759 | Find the projection of the vector $ \vec{v_1} = \left(5,~-1,~1\right) $ on the vector $ \vec{v_2} = \left(6,~7,~-6\right) $. | 1 |
| 2760 | Find the projection of the vector $ \vec{v_1} = \left(5,~7,~1\right) $ on the vector $ \vec{v_2} = \left(6,~-6,~1\right) $. | 1 |
| 2761 | Find the projection of the vector $ \vec{v_1} = \left(4,~6,~1\right) $ on the vector $ \vec{v_2} = \left(5,~-5,~1\right) $. | 1 |
| 2762 | Calculate the dot product of the vectors $ \vec{v_1} = \left(8,~-4\right) $ and $ \vec{v_2} = \left(1,~2\right) $ . | 1 |
| 2763 | Find the projection of the vector $ \vec{v_1} = \left(5,~7,~-1\right) $ on the vector $ \vec{v_2} = \left(6,~-6,~1\right) $. | 1 |
| 2764 | Calculate the dot product of the vectors $ \vec{v_1} = \left(4,~-1\right) $ and $ \vec{v_2} = \left(4,~-1\right) $ . | 1 |
| 2765 | Calculate the dot product of the vectors $ \vec{v_1} = \left(4,~-1\right) $ and $ \vec{v_2} = \left(1,~3\right) $ . | 1 |
| 2766 | Calculate the cross product of the vectors $ \vec{v_1} = \left(2,~-1,~8\right) $ and $ \vec{v_2} = \left(6,~2,~1\right) $ . | 1 |
| 2767 | Calculate the cross product of the vectors $ \vec{v_1} = \left(6,~2,~1\right) $ and $ \vec{v_2} = \left(2,~-1,~8\right) $ . | 1 |
| 2768 | Calculate the cross product of the vectors $ \vec{v_1} = \left(4,~3,~-3\right) $ and $ \vec{v_2} = \left(0,~3,~5\right) $ . | 1 |
| 2769 | Calculate the cross product of the vectors $ \vec{v_1} = \left(24,~-20,~12\right) $ and $ \vec{v_2} = \left(3,~0,~3\right) $ . | 1 |
| 2770 | Calculate the cross product of the vectors $ \vec{v_1} = \left(314,~-15,~6\right) $ and $ \vec{v_2} = \left(2,~0,~2\right) $ . | 1 |
| 2771 | Calculate the cross product of the vectors $ \vec{v_1} = \left(14,~-15,~6\right) $ and $ \vec{v_2} = \left(2,~0,~2\right) $ . | 1 |
| 2772 | Calculate the cross product of the vectors $ \vec{v_1} = \left(2,~0,~2\right) $ and $ \vec{v_2} = \left(14,~-15,~6\right) $ . | 1 |
| 2773 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-7,~1,~12\right) $ and $ \vec{v_2} = \left(2,~2,~3\right) $ . | 1 |
| 2774 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-4,~1,~4\right) $ and $ \vec{v_2} = \left(0,~2,~5\right) $ . | 1 |
| 2775 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-4,~10,~4\right) $ and $ \vec{v_2} = \left(0,~2,~5\right) $ . | 1 |
| 2776 | Find the sum of the vectors $ \vec{v_1} = \left(2,~-1.2\right) $ and $ \vec{v_2} = \left(6.19,~8.42\right) $ . | 1 |
| 2777 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~-2,~3\right) $ and $ \vec{v_2} = \left(3,~-2,~1\right) $ . | 1 |
| 2778 | Find the angle between vectors $ \left(6,~7\right)$ and $\left(7,~0\right)$. | 1 |
| 2779 | Calculate the dot product of the vectors $ \vec{v_1} = \left(4,~0\right) $ and $ \vec{v_2} = \left(-1,~4\right) $ . | 1 |
| 2780 | Find the angle between vectors $ \left(-\sqrt{ 3 },~1\right)$ and $\left(2,~-2 \sqrt{ 3 }\right)$. | 1 |
| 2781 | Find the angle between vectors $ \left(3,~5\right)$ and $\left(0,~1\right)$. | 1 |
| 2782 | Find the magnitude of the vector $ \| \vec{v} \| = \left(2,~1,~3\right) $ . | 1 |
| 2783 | Find the difference of the vectors $ \vec{v_1} = \left(200,~0\right) $ and $ \vec{v_2} = \left(20,~0\right) $ . | 1 |
| 2784 | Find the angle between vectors $ \left(200,~0\right)$ and $\left(20,~0\right)$. | 1 |
| 2785 | Find the angle between vectors $ \left(-4,~4\right)$ and $\left(-2,~4\right)$. | 1 |
| 2786 | Find the projection of the vector $ \vec{v_1} = \left(4,~-6\right) $ on the vector $ \vec{v_2} = \left(-2,~-5\right) $. | 1 |
| 2787 | Find the angle between vectors $ \left(-3,~-5\right)$ and $\left(0,~-2\right)$. | 1 |
| 2788 | Find the angle between vectors $ \left(\dfrac{ 1 }{ 4 },~\dfrac{ 1 }{ 4 }\right)$ and $\left(3,~-3\right)$. | 1 |
| 2789 | Find the angle between vectors $ \left(\dfrac{ 1 }{ 2 },~\dfrac{\sqrt{ 3 }}{ 2 }\right)$ and $\left(- \dfrac{\sqrt{ 2 }}{ 2 },~- \dfrac{\sqrt{ 2 }}{ 2 }\right)$. | 1 |
| 2790 | 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 |
| 2791 | Find the projection of the vector $ \vec{v_1} = \left(- \dfrac{\sqrt{ 2 }}{ 2 },~- \dfrac{\sqrt{ 2 }}{ 2 }\right) $ on the vector $ \vec{v_2} = \left(\dfrac{ 1 }{ 2 },~\dfrac{\sqrt{ 3 }}{ 2 }\right) $. | 1 |
| 2792 | Find the difference of the vectors $ \vec{v_1} = \left(\dfrac{ 1 }{ 2 },~\dfrac{\sqrt{ 3 }}{ 2 }\right) $ and $ \vec{v_2} = \left(\dfrac{\sqrt{ 11 }}{ 4 },~\dfrac{\sqrt{ 11 }}{ 4 }\right) $ . | 1 |
| 2793 | Find the magnitude of the vector $ \| \vec{v} \| = \left(5,~7\right) $ . | 1 |
| 2794 | Calculate the cross product of the vectors $ \vec{v_1} = \left(5,~6,~-5\right) $ and $ \vec{v_2} = \left(8,~0,~-7\right) $ . | 1 |
| 2795 | Calculate the cross product of the vectors $ \vec{v_1} = \left(3,~-1,~-4\right) $ and $ \vec{v_2} = \left(0,~0,~0\right) $ . | 1 |
| 2796 | Find the angle between vectors $ \left(2,~0,~-1\right)$ and $\left(2,~-1,~2\right)$. | 1 |
| 2797 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-3,~2,~-4\right) $ and $ \vec{v_2} = \left(3,~-4,~5\right) $ . | 1 |
| 2798 | Calculate the dot product of the vectors $ \vec{v_1} = \left(6,~2\right) $ and $ \vec{v_2} = \left(-2,~4\right) $ . | 1 |
| 2799 | Find the sum of the vectors $ \vec{v_1} = \left(-48,~-25,~20\right) $ and $ \vec{v_2} = \left(60,~30,~40\right) $ . | 1 |
| 2800 | Find the projection of the vector $ \vec{v_1} = \left(-48,~-25,~20\right) $ on the vector $ \vec{v_2} = \left(60,~30,~40\right) $. | 1 |
