Vectors – Solved Problems Database
All the problems and solutions shown below were generated using the Vectors Calculator.
ID |
Problem |
Count |
2751 | Find the magnitude of the vector $ \| \vec{v} \| = \left(1,~-2\right) $ . | 1 |
2752 | Find the projection of the vector $ \vec{v_1} = \left(\dfrac{ 5645117 }{ 100 },~-\dfrac{ 770859 }{ 50 },~\dfrac{ 429504 }{ 25 }\right) $ on the vector $ \vec{v_2} = \left(\dfrac{ 5643497 }{ 100 },~-\dfrac{ 1541283 }{ 100 },~\dfrac{ 858759 }{ 50 }\right) $. | 1 |
2753 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~1,~-4\right) $ and $ \vec{v_2} = \left(2,~2,~1\right) $ . | 1 |
2754 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-\dfrac{ 9 }{ 41 },~\dfrac{ 40 }{ 41 }\right) $ . | 1 |
2755 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-8,~-5\right) $ and $ \vec{v_2} = \left(-10,~-7\right) $ . | 1 |
2756 | Find the sum of the vectors $ \vec{v_1} = \left(10,~0\right) $ and $ \vec{v_2} = \left(12,~0\right) $ . | 1 |
2757 | Find the angle between vectors $ \left(-3,~4,~-5\right)$ and $\left(3,~4,~5\right)$. | 1 |
2758 | Find the sum of the vectors $ \vec{v_1} = \left(-47,~16\right) $ and $ \vec{v_2} = \left(10,~17\right) $ . | 1 |
2759 | | 1 |
2760 | Find the magnitude of the vector $ \| \vec{v} \| = \left(4,~1\right) $ . | 1 |
2761 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-2,~-1,~-3\right) $ and $ \vec{v_2} = \left(-1,~-2,~\dfrac{ 2 }{ 3 }\right) $ . | 1 |
2762 | Find the projection of the vector $ \vec{v_1} = \left(2,~2,~1\right) $ on the vector $ \vec{v_2} = \left(1,~-2,~0\right) $. | 1 |
2763 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~1,~1\right) $ and $ \vec{v_2} = \left(1,~1,~1\right) $ . | 1 |
2764 | Find the sum of the vectors $ \vec{v_1} = \left(9,~0\right) $ and $ \vec{v_2} = \left(1,~4\right) $ . | 1 |
2765 | Find the difference of the vectors $ \vec{v_1} = \left(-2,~3,~-1\right) $ and $ \vec{v_2} = \left(2,~1,~3\right) $ . | 1 |
2766 | Determine whether the vectors $ \vec{v_1} = \left(1,~4,~-2\right) $, $ \vec{v_2} = \left(6,~-2,~8\right) $ and $ \vec{v_3} = \left(0,~0,~0\right)$ are linearly independent or dependent. | 1 |
2767 | Find the magnitude of the vector $ \| \vec{v} \| = \left(24.35,~173.29\right) $ . | 1 |
2768 | Find the magnitude of the vector $ \| \vec{v} \| = \left(1,~-2,~3\right) $ . | 1 |
2769 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-1,~-2,~4\right) $ . | 1 |
2770 | Find the magnitude of the vector $ \| \vec{v} \| = \left(4,~8\right) $ . | 1 |
2771 | Calculate the dot product of the vectors $ \vec{v_1} = \left(0,~20,~12\right) $ and $ \vec{v_2} = \left(5,~-5,~-4\right) $ . | 1 |
2772 | Calculate the dot product of the vectors $ \vec{v_1} = \left(5,~4\right) $ and $ \vec{v_2} = \left(7,~3\right) $ . | 1 |
2773 | Find the sum of the vectors $ \vec{v_1} = \left(4,~6\right) $ and $ \vec{v_2} = \left(4,~1\right) $ . | 1 |
2774 | Find the sum of the vectors $ \vec{v_1} = \left(2,~3,~1\right) $ and $ \vec{v_2} = \left(0,~5,~4\right) $ . | 1 |
2775 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-9,~1\right) $ . | 1 |
2776 | Find the difference of the vectors $ \vec{v_1} = \left(-2,~4\right) $ and $ \vec{v_2} = \left(2,~-1\right) $ . | 1 |
2777 | Calculate the dot product of the vectors $ \vec{v_1} = \left(4,~-3\right) $ and $ \vec{v_2} = \left(3,~-3\right) $ . | 1 |
2778 | Find the magnitude of the vector $ \| \vec{v} \| = \left(6,~7,~3\right) $ . | 1 |
2779 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~2,~-1\right) $ and $ \vec{v_2} = \left(2,~1,~4\right) $ . | 1 |
2780 | Find the magnitude of the vector $ \| \vec{v} \| = \left(4,~-5,~6\right) $ . | 1 |
2781 | Calculate the dot product of the vectors $ \vec{v_1} = \left(0,~0,~1\right) $ and $ \vec{v_2} = \left(0,~0,~1\right) $ . | 1 |
2782 | Find the magnitude of the vector $ \| \vec{v} \| = \left(5,~-6,~0\right) $ . | 1 |
2783 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~1,~1\right) $ and $ \vec{v_2} = \left(0,~2,~1\right) $ . | 1 |
2784 | Find the magnitude of the vector $ \| \vec{v} \| = \left(\dfrac{ 9 }{ 41 },~\dfrac{ 40 }{ 41 }\right) $ . | 1 |
2785 | Find the difference of the vectors $ \vec{v_1} = \left(1,~0,~10\right) $ and $ \vec{v_2} = \left(5,~-5,~3\right) $ . | 1 |
2786 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~-2,~3\right) $ and $ \vec{v_2} = \left(5,~0,~2\right) $ . | 1 |
2787 | Calculate the cross product of the vectors $ \vec{v_1} = \left(2,~-6,~-3\right) $ and $ \vec{v_2} = \left(4,~3,~-1\right) $ . | 1 |
2788 | Find the sum of the vectors $ \vec{v_1} = \left(-1,~2,~-5\right) $ and $ \vec{v_2} = \left(1,~4,~-3\right) $ . | 1 |
2789 | Calculate the cross product of the vectors $ \vec{v_1} = \left(0,~20,~12\right) $ and $ \vec{v_2} = \left(5,~-5,~-4\right) $ . | 1 |
2790 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-1,~2,~3\right) $ and $ \vec{v_2} = \left(0,~2,~1\right) $ . | 1 |
2791 | Find the angle between vectors $ \left(1,~3,~-2\right)$ and $\left(-9,~1,~-5\right)$. | 1 |
2792 | Find the sum of the vectors $ \vec{v_1} = \left(-5,~2\right) $ and $ \vec{v_2} = \left(-4,~4\right) $ . | 1 |
2793 | Find the difference of the vectors $ \vec{v_1} = \left(-4,~8\right) $ and $ \vec{v_2} = \left(6,~-3\right) $ . | 1 |
2794 | Find the sum of the vectors $ \vec{v_1} = \left(\dfrac{ 3 }{ 5 },~-\dfrac{ 4 }{ 5 }\right) $ and $ \vec{v_2} = \left(\dfrac{ 4 }{ 5 },~\dfrac{ 2 }{ 5 }\right) $ . | 1 |
2795 | Calculate the cross product of the vectors $ \vec{v_1} = \left(0,~0,~0\right) $ and $ \vec{v_2} = \left(1,~-2,~3\right) $ . | 1 |
2796 | Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~5\right) $ and $ \vec{v_2} = \left(7,~-6\right) $ . | 1 |
2797 | Find the angle between vectors $ \left(4,~-3\right)$ and $\left(3,~-3\right)$. | 1 |
2798 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-2,~-1,~-3\right) $ and $ \vec{v_2} = \left(-1,~-2,~\dfrac{ 2 }{ 3 }\right) $ . | 1 |
2799 | Find the sum of the vectors $ \vec{v_1} = \left(-10,~8\right) $ and $ \vec{v_2} = \left(4,~-11\right) $ . | 1 |
2800 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-1,~0,~3\right) $ and $ \vec{v_2} = \left(1,~2,~-1\right) $ . | 1 |