Vectors – Solved Problems Database
All the problems and solutions shown below were generated using the Vectors Calculator.
ID |
Problem |
Count |
2851 | Find the sum of the vectors $ \vec{v_1} = \left(-2,~-10,~0\right) $ and $ \vec{v_2} = \left(10,~8,~0\right) $ . | 1 |
2852 | 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 |
2853 | Determine whether the vectors $ \vec{v_1} = \left(1,~-2,~3\right) $, $ \vec{v_2} = \left(5,~0,~2\right) $ and $ \vec{v_3} = \left(1,~-1,~3\right)$ are linearly independent or dependent. | 1 |
2854 | Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~1,~-2\right) $ and $ \vec{v_2} = \left(-3,~-1,~0\right) $ . | 1 |
2855 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-10,~13\right) $ . | 1 |
2856 | Calculate the cross product of the vectors $ \vec{v_1} = \left(7,~6,~6\right) $ and $ \vec{v_2} = \left(14,~-1,~13\right) $ . | 1 |
2857 | 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 |
2858 | Find the difference of the vectors $ \vec{v_1} = \left(1,~2\right) $ and $ \vec{v_2} = \left(-4,~12\right) $ . | 1 |
2859 | Calculate the cross product of the vectors $ \vec{v_1} = \left(9,~-6,~3\right) $ and $ \vec{v_2} = \left(-4,~4,~2\right) $ . | 1 |
2860 | Find the angle between vectors $ \left(54.9123,~23.9363\right)$ and $\left(54.9276,~23.9704\right)$. | 1 |
2861 | Find the projection of the vector $ \vec{v_1} = \left(2,~5\right) $ on the vector $ \vec{v_2} = \left(-4,~-2\right) $. | 1 |
2862 | 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(0,~-2,~-2\right) $ . | 1 |
2863 | Find the sum of the vectors $ \vec{v_1} = \left(4,~3\right) $ and $ \vec{v_2} = \left(-2,~2\right) $ . | 1 |
2864 | Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~3,~-2\right) $ and $ \vec{v_2} = \left(-1,~-4,~2\right) $ . | 1 |
2865 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~2,~3\right) $ and $ \vec{v_2} = \left(2,~5,~7\right) $ . | 1 |
2866 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~-2,~0\right) $ and $ \vec{v_2} = \left(0,~1,~2\right) $ . | 1 |
2867 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-13,~-3,~1\right) $ and $ \vec{v_2} = \left(-12,~1,~5\right) $ . | 1 |
2868 | Find the magnitude of the vector $ \| \vec{v} \| = \left(37.8,~39.6\right) $ . | 1 |
2869 | Find the difference of the vectors $ \vec{v_1} = \left(\dfrac{ 3489 }{ 10000 },~\dfrac{ 6199 }{ 10000 },~\dfrac{ 1927 }{ 5000 }\right) $ and $ \vec{v_2} = \left(\dfrac{ 359 }{ 1000 },~\dfrac{ 65487 }{ 100000 },~\dfrac{ 22241 }{ 50000 }\right) $ . | 1 |
2870 | Determine whether the vectors $ \vec{v_1} = \left(1,~2,~6\right) $, $ \vec{v_2} = \left(2,~5,~14\right) $ and $ \vec{v_3} = \left(5,~7,~24\right)$ are linearly independent or dependent. | 1 |
2871 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~2,~-4\right) $ and $ \vec{v_2} = \left(-5,~3,~-7\right) $ . | 1 |
2872 | Calculate the dot product of the vectors $ \vec{v_1} = \left(6,~7\right) $ and $ \vec{v_2} = \left(9,~1\right) $ . | 1 |
2873 | Find the sum of the vectors $ \vec{v_1} = \left(\dfrac{ 6 }{ 5 },~-\dfrac{ 12 }{ 5 }\right) $ and $ \vec{v_2} = \left(28,~96\right) $ . | 1 |
2874 | Calculate the dot product of the vectors $ \vec{v_1} = \left(255,~255\right) $ and $ \vec{v_2} = \left(-150,~-300\right) $ . | 1 |
2875 | Find the magnitude of the vector $ \| \vec{v} \| = \left(4,~-8\right) $ . | 1 |
2876 | Determine whether the vectors $ \vec{v_1} = \left(2,~5\right) $ and $ \vec{v_2} = \left(-4,~-2\right) $ are linearly independent or dependent. | 1 |
2877 | Find the magnitude of the vector $ \| \vec{v} \| = \left(4,~2\right) $ . | 1 |
2878 | Find the angle between vectors $ \left(2,~3,~2\right)$ and $\left(-1,~4,~-3\right)$. | 1 |
2879 | 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(0,~-2,~-2\right) $. | 1 |
2880 | | 1 |
2881 | Find the angle between vectors $ \left(6,~6,~-3\right)$ and $\left(6,~3,~6\right)$. | 1 |
2882 | Find the magnitude of the vector $ \| \vec{v} \| = \left(9,~8\right) $ . | 1 |
2883 | Find the angle between vectors $ \left(-9,~12,~0\right)$ and $\left(0,~20,~0\right)$. | 1 |
2884 | Find the sum of the vectors $ \vec{v_1} = \left(3,~2\right) $ and $ \vec{v_2} = \left(8,~-4\right) $ . | 1 |
2885 | Find the angle between vectors $ \left(-7,~-2\right)$ and $\left(-6,~-5\right)$. | 1 |
2886 | Calculate the dot product of the vectors $ \vec{v_1} = \left(4,~10,~4\right) $ and $ \vec{v_2} = \left(0,~12,~2\right) $ . | 1 |
2887 | Find the magnitude of the vector $ \| \vec{v} \| = \left(6,~0,~8\right) $ . | 1 |
2888 | Find the angle between vectors $ \left(6,~7\right)$ and $\left(9,~1\right)$. | 1 |
2889 | Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~-2,~4\right) $ and $ \vec{v_2} = \left(3,~-6,~-2\right) $ . | 1 |
2890 | Find the projection of the vector $ \vec{v_1} = \left(1,~1,~2\right) $ on the vector $ \vec{v_2} = \left(-2,~3,~1\right) $. | 1 |
2891 | Find the magnitude of the vector $ \| \vec{v} \| = \left(4,~0,~3\right) $ . | 1 |
2892 | Find the difference of the vectors $ \vec{v_1} = \left(3,~5\right) $ and $ \vec{v_2} = \left(6,~0\right) $ . | 1 |
2893 | Calculate the dot product of the vectors $ \vec{v_1} = \left(4,~2,~-1\right) $ and $ \vec{v_2} = \left(1,~-3,~5\right) $ . | 1 |
2894 | Find the sum of the vectors $ \vec{v_1} = \left(2,~5\right) $ and $ \vec{v_2} = \left(-4,~-2\right) $ . | 1 |
2895 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~1,~0\right) $ and $ \vec{v_2} = \left(2,~0,~3\right) $ . | 1 |
2896 | Find the angle between vectors $ \left(5,~5\right)$ and $\left(-8,~8\right)$. | 1 |
2897 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~2,~3\right) $ and $ \vec{v_2} = \left(1,~1,~2\right) $ . | 1 |
2898 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-59,~-119\right) $ . | 1 |
2899 | Find the difference of the vectors $ \vec{v_1} = \left(2,~1,~-1\right) $ and $ \vec{v_2} = \left(4,~3,~-2\right) $ . | 1 |
2900 | Find the angle between vectors $ \left(3,~4\right)$ and $\left(-7,~24\right)$. | 1 |