Vectors – Solved Problems Database
All the problems and solutions shown below were generated using the Vectors Calculator.
ID |
Problem |
Count |
2951 | Find the difference of the vectors $ \vec{v_1} = \left(3,~7,~19\right) $ and $ \vec{v_2} = \left(6,~16,~13\right) $ . | 1 |
2952 | Find the magnitude of the vector $ \| \vec{v} \| = \left(24.35,~173.29\right) $ . | 1 |
2953 | Calculate the dot product of the vectors $ \vec{v_1} = \left(8,~4\right) $ and $ \vec{v_2} = \left(-6,~5\right) $ . | 1 |
2954 | Calculate the cross product of the vectors $ \vec{v_1} = \left(3,~-1,~1\right) $ and $ \vec{v_2} = \left(-3,~3,~-2\right) $ . | 1 |
2955 | Calculate the dot product of the vectors $ \vec{v_1} = \left(0,~-2\right) $ and $ \vec{v_2} = \left(5,~1\right) $ . | 1 |
2956 | Find the sum of the vectors $ \vec{v_1} = \left(-\dfrac{ 8 }{ 9 },~-\dfrac{ 14 }{ 9 }\right) $ and $ \vec{v_2} = \left(30,~135\right) $ . | 1 |
2957 | Calculate the dot product of the vectors $ \vec{v_1} = \left(0,~0\right) $ and $ \vec{v_2} = \left(0,~0\right) $ . | 1 |
2958 | Find the magnitude of the vector $ \| \vec{v} \| = \left(5,~5 \sqrt{ 2 },~5\right) $ . | 1 |
2959 | Find the angle between vectors $ \left(2,~2\right)$ and $\left(1,~3\right)$. | 1 |
2960 | | 1 |
2961 | Find the angle between vectors $ \left(2,~-3,~2\right)$ and $\left(3,~-1,~4\right)$. | 1 |
2962 | Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~-1,~4\right) $ and $ \vec{v_2} = \left(0,~3,~-1\right) $ . | 1 |
2963 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-3,~1,~5\right) $ . | 1 |
2964 | Find the magnitude of the vector $ \| \vec{v} \| = \left(0,~5\right) $ . | 1 |
2965 | Find the sum of the vectors $ \vec{v_1} = \left(2,~5\right) $ and $ \vec{v_2} = \left(3,~4\right) $ . | 1 |
2966 | Find the angle between vectors $ \left(2,~4,~-1\right)$ and $\left(-3,~0,~6\right)$. | 1 |
2967 | Calculate the cross product of the vectors $ \vec{v_1} = \left(31,~-22,~39\right) $ and $ \vec{v_2} = \left(40,~17,~46\right) $ . | 1 |
2968 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-\dfrac{ 371 }{ 50 },~0\right) $ . | 1 |
2969 | Find the magnitude of the vector $ \| \vec{v} \| = \left(\dfrac{ 1 }{ 2 },~\dfrac{ 49 }{ 10 },~30\right) $ . | 1 |
2970 | Calculate the dot product of the vectors $ \vec{v_1} = \left(\dfrac{ 43 }{ 5 },~1,~7\right) $ and $ \vec{v_2} = \left(\dfrac{ 49 }{ 5 },~\dfrac{ 19 }{ 2 },~\dfrac{ 29 }{ 10 }\right) $ . | 1 |
2971 | Find the magnitude of the vector $ \| \vec{v} \| = \left(0.2,~0.2,~0.2\right) $ . | 1 |
2972 | Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~-2\right) $ and $ \vec{v_2} = \left(5,~-5\right) $ . | 1 |
2973 | 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 |
2974 | Find the angle between vectors $ \left(-4,~4\right)$ and $\left(-2,~4\right)$. | 1 |
2975 | Calculate the cross product of the vectors $ \vec{v_1} = \left(2,~-2,~1\right) $ and $ \vec{v_2} = \left(2,~1,~2\right) $ . | 1 |
2976 | Find the magnitude of the vector $ \| \vec{v} \| = \left(12,~3\right) $ . | 1 |
2977 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~0,~0\right) $ and $ \vec{v_2} = \left(0,~-0.0349,~0.9994\right) $ . | 1 |
2978 | Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~-5,~5\right) $ and $ \vec{v_2} = \left(2,~-5,~5\right) $ . | 1 |
2979 | Calculate the dot product of the vectors $ \vec{v_1} = \left(6,~10\right) $ and $ \vec{v_2} = \left(-1,~5\right) $ . | 1 |
2980 | Calculate the dot product of the vectors $ \vec{v_1} = \left(7,~5,~-4\right) $ and $ \vec{v_2} = \left(-1,~3,~6\right) $ . | 1 |
2981 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-17,~-3,~2\right) $ . | 1 |
2982 | Find the sum of the vectors $ \vec{v_1} = \left(3,~4\right) $ and $ \vec{v_2} = \left(2,~8\right) $ . | 1 |
2983 | Find the sum of the vectors $ \vec{v_1} = \left(1,~3\right) $ and $ \vec{v_2} = \left(6,~10\right) $ . | 1 |
2984 | Find the angle between vectors $ \left(-\dfrac{ 46 }{ 5 },~-\dfrac{ 22 }{ 5 },~-\dfrac{ 6 }{ 5 }\right)$ and $\left(-\dfrac{ 44 }{ 5 },~\dfrac{ 67 }{ 10 },~\dfrac{ 27 }{ 10 }\right)$. | 1 |
2985 | Find the magnitude of the vector $ \| \vec{v} \| = \left(5,~0\right) $ . | 1 |
2986 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~9,~-3\right) $ and $ \vec{v_2} = \left(1,~2,~-4\right) $ . | 1 |
2987 | Calculate the cross product of the vectors $ \vec{v_1} = \left(7,~-2,~1\right) $ and $ \vec{v_2} = \left(-6,~4,~9\right) $ . | 1 |
2988 | Calculate the cross product of the vectors $ \vec{v_1} = \left(3,~4,~4\right) $ and $ \vec{v_2} = \left(0,~1,~2\right) $ . | 1 |
2989 | Calculate the cross product of the vectors $ \vec{v_1} = \left(2,~3,~2\right) $ and $ \vec{v_2} = \left(-1,~4,~-3\right) $ . | 1 |
2990 | Find the sum of the vectors $ \vec{v_1} = \left(4,~5\right) $ and $ \vec{v_2} = \left(-3,~5\right) $ . | 1 |
2991 | Calculate the cross product of the vectors $ \vec{v_1} = \left(2,~-3,~0\right) $ and $ \vec{v_2} = \left(-1,~2,~-4\right) $ . | 1 |
2992 | Calculate the cross product of the vectors $ \vec{v_1} = \left(4,~0,~3\right) $ and $ \vec{v_2} = \left(0,~-2,~-5\right) $ . | 1 |
2993 | Find the sum of the vectors $ \vec{v_1} = \left(10,~0\right) $ and $ \vec{v_2} = \left(-14.3,~-2.34\right) $ . | 1 |
2994 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-4,~2,~2\right) $ and $ \vec{v_2} = \left(2,~-3,~1\right) $ . | 1 |
2995 | Calculate the dot product of the vectors $ \vec{v_1} = \left(0,~5,~3\right) $ and $ \vec{v_2} = \left(1,~7,~6\right) $ . | 1 |
2996 | Calculate the cross product of the vectors $ \vec{v_1} = \left(7,~-7,~9\right) $ and $ \vec{v_2} = \left(9,~4,~-10\right) $ . | 1 |
2997 | Find the sum of the vectors $ \vec{v_1} = \left(2,~1,~-1\right) $ and $ \vec{v_2} = \left(-1,~-2,~5\right) $ . | 1 |
2998 | Find the sum of the vectors $ \vec{v_1} = \left(-1,~5\right) $ and $ \vec{v_2} = \left(0,~-4\right) $ . | 1 |
2999 | Find the magnitude of the vector $ \| \vec{v} \| = \left(2,~-1\right) $ . | 1 |
3000 | Calculate the cross product of the vectors $ \vec{v_1} = \left(4,~2,~-2\right) $ and $ \vec{v_2} = \left(1,~5,~5\right) $ . | 1 |