Vectors – Solved Problems Database
All the problems and solutions shown below were generated using the Vectors Calculator.
ID |
Problem |
Count |
2801 | Calculate the dot product of the vectors $ \vec{v_1} = \left(5,~5\right) $ and $ \vec{v_2} = \left(-6,~1\right) $ . | 1 |
2802 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~1,~1\right) $ and $ \vec{v_2} = \left(0,~2,~1\right) $ . | 1 |
2803 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-7,~-1,~2\right) $ and $ \vec{v_2} = \left(-1,~1,~5\right) $ . | 1 |
2804 | Find the magnitude of the vector $ \| \vec{v} \| = \left(2,~4,~6\right) $ . | 1 |
2805 | Determine whether the vectors $ \vec{v_1} = \left(2,~5\right) $ and $ \vec{v_2} = \left(-2,~1\right) $ are linearly independent or dependent. | 1 |
2806 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~-2,~3\right) $ and $ \vec{v_2} = \left(5,~0,~2\right) $ . | 1 |
2807 | Find the difference of the vectors $ \vec{v_1} = \left(1,~2\right) $ and $ \vec{v_2} = \left(4,~7\right) $ . | 1 |
2808 | Calculate the cross product of the vectors $ \vec{v_1} = \left(2,~-3,~1\right) $ and $ \vec{v_2} = \left(-3,~3,~2\right) $ . | 1 |
2809 | Find the sum of the vectors $ \vec{v_1} = \left(3,~5,~-6\right) $ and $ \vec{v_2} = \left(1,~-3,~5\right) $ . | 1 |
2810 | Find the projection of the vector $ \vec{v_1} = \left(1,~1,~1\right) $ on the vector $ \vec{v_2} = \left(0,~2,~1\right) $. | 1 |
2811 | Find the difference of the vectors $ \vec{v_1} = \left(2,~5\right) $ and $ \vec{v_2} = \left(4,~7\right) $ . | 1 |
2812 | Find the projection of the vector $ \vec{v_1} = \left(2,~4,~6\right) $ on the vector $ \vec{v_2} = \left(1,~3,~5\right) $. | 1 |
2813 | Determine whether the vectors $ \vec{v_1} = \left(25,~64,~144\right) $, $ \vec{v_2} = \left(5,~8,~12\right) $ and $ \vec{v_3} = \left(1,~1,~1\right)$ are linearly independent or dependent. | 1 |
2814 | Find the sum of the vectors $ \vec{v_1} = \left(1,~-2,~3\right) $ and $ \vec{v_2} = \left(5,~0,~2\right) $ . | 1 |
2815 | Calculate the cross product of the vectors $ \vec{v_1} = \left(2,~3,~-2\right) $ and $ \vec{v_2} = \left(2,~0,~3\right) $ . | 1 |
2816 | Find the angle between vectors $ \left(2,~0\right)$ and $\left(3,~8\right)$. | 1 |
2817 | Find the magnitude of the vector $ \| \vec{v} \| = \left(4,~1\right) $ . | 1 |
2818 | Find the difference of the vectors $ \vec{v_1} = \left(-4,~4\right) $ and $ \vec{v_2} = \left(4,~-3\right) $ . | 1 |
2819 | Determine whether the vectors $ \vec{v_1} = \left(2,~1,~-2\right) $, $ \vec{v_2} = \left(1,~0,~0\right) $ and $ \vec{v_3} = \left(0,~0,~0\right)$ are linearly independent or dependent. | 1 |
2820 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-4,~-6,~-\dfrac{ 2 }{ 3 }\right) $ and $ \vec{v_2} = \left(4,~-3,~-1\right) $ . | 1 |
2821 | Find the projection of the vector $ \vec{v_1} = \left(\dfrac{\sqrt{ 2 }}{ 2 },~\dfrac{\sqrt{ 2 }}{ 2 },~0\right) $ on the vector $ \vec{v_2} = \left(-1,~1,~-1\right) $. | 1 |
2822 | Find the magnitude of the vector $ \| \vec{v} \| = \left(2,~5\right) $ . | 1 |
2823 | Find the difference of the vectors $ \vec{v_1} = \left(1,~-2,~3\right) $ and $ \vec{v_2} = \left(5,~0,~2\right) $ . | 1 |
2824 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-2,~1,~3\right) $ . | 1 |
2825 | Find the projection of the vector $ \vec{v_1} = \left(407,~-4,~288\right) $ on the vector $ \vec{v_2} = \left(0,~0,~0\right) $. | 1 |
2826 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-2,~-1,~1\right) $ and $ \vec{v_2} = \left(3,~-1,~-1\right) $ . | 1 |
2827 | Find the magnitude of the vector $ \| \vec{v} \| = \left(9,~30\right) $ . | 1 |
2828 | Find the sum of the vectors $ \vec{v_1} = \left(4,~2,~-1\right) $ and $ \vec{v_2} = \left(1,~-3,~5\right) $ . | 1 |
2829 | Find the angle between vectors $ \left(1,~1\right)$ and $\left(4,~4\right)$. | 1 |
2830 | Find the angle between vectors $ \left(2,~5\right)$ and $\left(-4,~-2\right)$. | 1 |
2831 | Calculate the dot product of the vectors $ \vec{v_1} = \left(\dfrac{\sqrt{ 2 }}{ 2 },~\dfrac{\sqrt{ 2 }}{ 2 },~0\right) $ and $ \vec{v_2} = \left(-1,~1,~-1\right) $ . | 1 |
2832 | Calculate the cross product of the vectors $ \vec{v_1} = \left(4,~3,~6\right) $ and $ \vec{v_2} = \left(-1,~3,~-8\right) $ . | 1 |
2833 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-9,~-7\right) $ . | 1 |
2834 | Find the magnitude of the vector $ \| \vec{v} \| = \left(2,~6,~8\right) $ . | 1 |
2835 | Find the magnitude of the vector $ \| \vec{v} \| = \left(3,~2,~7\right) $ . | 1 |
2836 | Find the angle between vectors $ \left(2,~5\right)$ and $\left(-2,~1\right)$. | 1 |
2837 | Find the magnitude of the vector $ \| \vec{v} \| = \left(4,~2,~-12\right) $ . | 1 |
2838 | Find the angle between vectors $ \left(1,~-2,~3\right)$ and $\left(5,~0,~2\right)$. | 1 |
2839 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~6,~-8\right) $ and $ \vec{v_2} = \left(4,~-2,~-1\right) $ . | 1 |
2840 | Find the magnitude of the vector $ \| \vec{v} \| = \left(\dfrac{ 6 }{ 5 },~-\dfrac{ 12 }{ 5 }\right) $ . | 1 |
2841 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-\dfrac{ 9 }{ 41 },~\dfrac{ 40 }{ 41 }\right) $ . | 1 |
2842 | Calculate the dot product of the vectors $ \vec{v_1} = \left(6,~0\right) $ and $ \vec{v_2} = \left(5,~45\right) $ . | 1 |
2843 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-4,~3\right) $ and $ \vec{v_2} = \left(0,~4\right) $ . | 1 |
2844 | Calculate the dot product of the vectors $ \vec{v_1} = \left(6,~3\right) $ and $ \vec{v_2} = \left(-6,~12\right) $ . | 1 |
2845 | Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~1,~-2\right) $ and $ \vec{v_2} = \left(1,~0,~0\right) $ . | 1 |
2846 | Calculate the cross product of the vectors $ \vec{v_1} = \left(4,~2,~-1\right) $ and $ \vec{v_2} = \left(1,~-3,~5\right) $ . | 1 |
2847 | Find the magnitude of the vector $ \| \vec{v} \| = \left(2,~5\right) $ . | 1 |
2848 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-8,~-5\right) $ . | 1 |
2849 | Find the angle between vectors $ \left(1,~1,~0\right)$ and $\left(2,~0,~3\right)$. | 1 |
2850 | Determine whether the vectors $ \vec{v_1} = \left(-3,~-1\right) $ and $ \vec{v_2} = \left(-9,~-2\right) $ are linearly independent or dependent. | 1 |