Vectors – Solved Problems Database
All the problems and solutions shown below were generated using the Vectors Calculator.
ID |
Problem |
Count |
2901 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-3,~4,~3\right) $ and $ \vec{v_2} = \left(4,~3,~4\right) $ . | 1 |
2902 | Find the projection of the vector $ \vec{v_1} = \left(3,~-3\right) $ on the vector $ \vec{v_2} = \left(4,~9\right) $. | 1 |
2903 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-10,~-21,~4\right) $ . | 1 |
2904 | Find the difference of the vectors $ \vec{v_1} = \left(0,~-5\right) $ and $ \vec{v_2} = \left(-6,~-8\right) $ . | 1 |
2905 | Find the projection of the vector $ \vec{v_1} = \left(\dfrac{ 219 }{ 10 },~1,~-\dfrac{ 15 }{ 2 }\right) $ on the vector $ \vec{v_2} = \left(0,~0,~0\right) $. | 1 |
2906 | Find the magnitude of the vector $ \| \vec{v} \| = \left(\dfrac{ 101 }{ 10000 },~\dfrac{ 3497 }{ 100000 },~\dfrac{ 2971 }{ 50000 }\right) $ . | 1 |
2907 | Find the difference of the vectors $ \vec{v_1} = \left(7,~-3\right) $ and $ \vec{v_2} = \left(7,~-8\right) $ . | 1 |
2908 | Find the angle between vectors $ \left(255,~255\right)$ and $\left(-150,~-300\right)$. | 1 |
2909 | Find the difference of the vectors $ \vec{v_1} = \left(2,~2\right) $ and $ \vec{v_2} = \left(4,~7\right) $ . | 1 |
2910 | Find the sum of the vectors $ \vec{v_1} = \left(-8,~\sqrt{ 7 }\right) $ and $ \vec{v_2} = \left(64,~36\right) $ . | 1 |
2911 | Find the magnitude of the vector $ \| \vec{v} \| = \left(3,~8\right) $ . | 1 |
2912 | Find the projection of the vector $ \vec{v_1} = \left(-1,~1,~-1\right) $ on the vector $ \vec{v_2} = \left(0,~-2,~-2\right) $. | 1 |
2913 | Find the angle between vectors $ \left(800,~0,~0\right)$ and $\left(847,~0,~0\right)$. | 1 |
2914 | Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~-3,~0\right) $ and $ \vec{v_2} = \left(-1,~2,~-4\right) $ . | 1 |
2915 | Find the sum of the vectors $ \vec{v_1} = \left(6,~1\right) $ and $ \vec{v_2} = \left(1,~5\right) $ . | 1 |
2916 | Calculate the cross product of the vectors $ \vec{v_1} = \left(2,~1,~-2\right) $ and $ \vec{v_2} = \left(1,~2,~1\right) $ . | 1 |
2917 | Find the difference of the vectors $ \vec{v_1} = \left(\dfrac{ 1531 }{ 5 },~\dfrac{ 71 }{ 5 },~-\dfrac{ 621 }{ 5 }\right) $ and $ \vec{v_2} = \left(\dfrac{ 1827 }{ 10 },~\dfrac{ 99 }{ 5 },~-\dfrac{ 752 }{ 5 }\right) $ . | 1 |
2918 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-2 \sqrt{ 6 },~5\right) $ . | 1 |
2919 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-10,~-29,~-4\right) $ . | 1 |
2920 | Find the sum of the vectors $ \vec{v_1} = \left(2,~-1,~1\right) $ and $ \vec{v_2} = \left(4,~3,~-5\right) $ . | 1 |
2921 | Find the magnitude of the vector $ \| \vec{v} \| = \left(6,~-5,~-3\right) $ . | 1 |
2922 | Find the projection of the vector $ \vec{v_1} = \left(1,~0,~3\right) $ on the vector $ \vec{v_2} = \left(1,~2,~-1\right) $. | 1 |
2923 | Find the angle between vectors $ \left(4,~0\right)$ and $\left(3,~2\right)$. | 1 |
2924 | Determine whether the vectors $ \vec{v_1} = \left(1,~1,~-2\right) $, $ \vec{v_2} = \left(-2,~1,~1\right) $ and $ \vec{v_3} = \left(1,~-1,~0\right)$ are linearly independent or dependent. | 1 |
2925 | Find the magnitude of the vector $ \| \vec{v} \| = \left(6,~-2,~3\right) $ . | 1 |
2926 | Find the difference of the vectors $ \vec{v_1} = \left(0,~0\right) $ and $ \vec{v_2} = \left(0,~3\right) $ . | 1 |
2927 | Find the projection of the vector $ \vec{v_1} = \left(4,~1,~-3\right) $ on the vector $ \vec{v_2} = \left(\dfrac{ 1 }{ 3 },~-\dfrac{ 2 }{ 3 },~\dfrac{ 2 }{ 3 }\right) $. | 1 |
2928 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~2,~-7\right) $ and $ \vec{v_2} = \left(5,~1,~1\right) $ . | 1 |
2929 | Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~-5,~5\right) $ and $ \vec{v_2} = \left(4,~-5,~-3\right) $ . | 1 |
2930 | Find the magnitude of the vector $ \| \vec{v} \| = \left(3,~-1\right) $ . | 1 |
2931 | Find the difference of the vectors $ \vec{v_1} = \left(-2,~0,~-3\right) $ and $ \vec{v_2} = \left(-4,~-6,~1\right) $ . | 1 |
2932 | Find the angle between vectors $ \left(2,~1,~-3\right)$ and $\left(4,~-2,~6\right)$. | 1 |
2933 | Find the magnitude of the vector $ \| \vec{v} \| = \left(0,~-2\right) $ . | 1 |
2934 | Find the sum of the vectors $ \vec{v_1} = \left(5,~2\right) $ and $ \vec{v_2} = \left(9,~7\right) $ . | 1 |
2935 | 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 |
2936 | Find the angle between vectors $ \left(2,~1\right)$ and $\left(2,~3\right)$. | 1 |
2937 | Calculate the cross product of the vectors $ \vec{v_1} = \left(2,~1,~-2\right) $ and $ \vec{v_2} = \left(1,~0,~0\right) $ . | 1 |
2938 | Find the difference of the vectors $ \vec{v_1} = \left(-8,~\sqrt{ 7 }\right) $ and $ \vec{v_2} = \left(64,~36\right) $ . | 1 |
2939 | Find the magnitude of the vector $ \| \vec{v} \| = \left(6,~-2,~3\right) $ . | 1 |
2940 | Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~2,~\sqrt{ 5 }\right) $ and $ \vec{v_2} = \left(-3,~-4,~-\sqrt{ 5 }\right) $ . | 1 |
2941 | Find the sum of the vectors $ \vec{v_1} = \left(7,~-4\right) $ and $ \vec{v_2} = \left(-3,~-5\right) $ . | 1 |
2942 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-2,~1,~-3\right) $ and $ \vec{v_2} = \left(-1,~-3,~-5\right) $ . | 1 |
2943 | Find the difference of the vectors $ \vec{v_1} = \left(-4,~10\right) $ and $ \vec{v_2} = \left(-12,~-3\right) $ . | 1 |
2944 | Find the angle between vectors $ \left(0,~5\right)$ and $\left(4,~0\right)$. | 1 |
2945 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-5,~0\right) $ . | 1 |
2946 | Find the magnitude of the vector $ \| \vec{v} \| = \left(9,~-36,~-9\right) $ . | 1 |
2947 | Find the angle between vectors $ \left(-1,~-2\right)$ and $\left(-2,~3\right)$. | 1 |
2948 | Calculate the dot product of the vectors $ \vec{v_1} = \left(0,~0,~1\right) $ and $ \vec{v_2} = \left(0,~0,~0\right) $ . | 1 |
2949 | Find the angle between vectors $ \left(3,~-1\right)$ and $\left(2,~7\right)$. | 1 |
2950 | Calculate the cross product of the vectors $ \vec{v_1} = \left(61,~-25,~8\right) $ and $ \vec{v_2} = \left(-6,~4,~-8\right) $ . | 1 |