Vectors – Solved Problems Database
All the problems and solutions shown below were generated using the Vectors Calculator.
ID |
Problem |
Count |
3051 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-3,~9\right) $ . | 1 |
3052 | Calculate the cross product of the vectors $ \vec{v_1} = \left(3,~4,~-7\right) $ and $ \vec{v_2} = \left(1,~1,~-1\right) $ . | 1 |
3053 | Find the difference of the vectors $ \vec{v_1} = \left(-5,~6\right) $ and $ \vec{v_2} = \left(3,~6\right) $ . | 1 |
3054 | Find the angle between vectors $ \left(3,~2,~5\right)$ and $\left(4,~1,~3\right)$. | 1 |
3055 | Calculate the cross product of the vectors $ \vec{v_1} = \left(11.44,~0,~0\right) $ and $ \vec{v_2} = \left(1.8,~-3.4,~0\right) $ . | 1 |
3056 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-8,~12,~4\right) $ and $ \vec{v_2} = \left(6,~-9,~-3\right) $ . | 1 |
3057 | Find the sum of the vectors $ \vec{v_1} = \left(12,~27\right) $ and $ \vec{v_2} = \left(8,~0\right) $ . | 1 |
3058 | Find the difference of the vectors $ \vec{v_1} = \left(4,~2\right) $ and $ \vec{v_2} = \left(2,~4\right) $ . | 1 |
3059 | Find the difference of the vectors $ \vec{v_1} = \left(1,~-2\right) $ and $ \vec{v_2} = \left(5,~-4\right) $ . | 1 |
3060 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-8,~-3\right) $ . | 1 |
3061 | Find the magnitude of the vector $ \| \vec{v} \| = \left(2,~5\right) $ . | 1 |
3062 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-1,~0,~0\right) $ . | 1 |
3063 | Calculate the cross product of the vectors $ \vec{v_1} = \left(2,~1,~0\right) $ and $ \vec{v_2} = \left(-3,~2,~0\right) $ . | 1 |
3064 | Find the angle between vectors $ \left(2,~1,~3\right)$ and $\left(-4,~5,~7\right)$. | 1 |
3065 | Find the angle between vectors $ \left(2,~7\right)$ and $\left(3,~0\right)$. | 1 |
3066 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~1,~-1\right) $ and $ \vec{v_2} = \left(3,~4,~-7\right) $ . | 1 |
3067 | Find the sum of the vectors $ \vec{v_1} = \left(3,~4\right) $ and $ \vec{v_2} = \left(1,~2\right) $ . | 1 |
3068 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-\dfrac{ 83 }{ 10 },~\dfrac{ 27 }{ 10 },~\dfrac{ 27 }{ 10 }\right) $ and $ \vec{v_2} = \left(-3,~\dfrac{ 33 }{ 5 },~\dfrac{ 31 }{ 10 }\right) $ . | 1 |
3069 | Find the projection of the vector $ \vec{v_1} = \left(4,~-6\right) $ on the vector $ \vec{v_2} = \left(-2,~-5\right) $. | 1 |
3070 | Find the angle between vectors $ \left(3806.5,~1774.9\right)$ and $\left(2544.1,~-1589.7\right)$. | 1 |
3071 | Calculate the dot product of the vectors $ \vec{v_1} = \left(7,~5\right) $ and $ \vec{v_2} = \left(-9,~7\right) $ . | 1 |
3072 | Find the sum of the vectors $ \vec{v_1} = \left(5,~3\right) $ and $ \vec{v_2} = \left(4,~-6\right) $ . | 1 |
3073 | Find the angle between vectors $ \left(-8,~12,~4\right)$ and $\left(6,~-9,~-3\right)$. | 1 |
3074 | Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~-5\right) $ and $ \vec{v_2} = \left(-1,~5\right) $ . | 1 |
3075 | Find the magnitude of the vector $ \| \vec{v} \| = \left(\dfrac{ 1 }{ 9 },~\dfrac{ 8 }{ 9 }\right) $ . | 1 |
3076 | Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~\dfrac{ 3 }{ 2 }\right) $ and $ \vec{v_2} = \left(-3,~4\right) $ . | 1 |
3077 | Find the projection of the vector $ \vec{v_1} = \left(3,~2\right) $ on the vector $ \vec{v_2} = \left(1,~3\right) $. | 1 |
3078 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-5,~-2,~3\right) $ and $ \vec{v_2} = \left(3,~-5,~4\right) $ . | 1 |
3079 | Find the sum of the vectors $ \vec{v_1} = \left(-4,~0,~1\right) $ and $ \vec{v_2} = \left(1,~6,~-2\right) $ . | 1 |
3080 | Find the angle between vectors $ \left(-1,~1,~-1\right)$ and $\left(1,~-1,~1\right)$. | 1 |
3081 | Calculate the cross product of the vectors $ \vec{v_1} = \left(2,~-1,~3\right) $ and $ \vec{v_2} = \left(-4,~2,~1\right) $ . | 1 |
3082 | Find the angle between vectors $ \left(-7,~6\right)$ and $\left(-7,~-4\right)$. | 1 |
3083 | Calculate the cross product of the vectors $ \vec{v_1} = \left(5,~-1,~6\right) $ and $ \vec{v_2} = \left(5,~-5,~-2\right) $ . | 1 |
3084 | Find the angle between vectors $ \left(1,~0\right)$ and $\left(0,~-5\right)$. | 1 |
3085 | Calculate the cross product of the vectors $ \vec{v_1} = \left(4,~-2,~2\right) $ and $ \vec{v_2} = \left(1,~0,~1\right) $ . | 1 |
3086 | Find the magnitude of the vector $ \| \vec{v} \| = \left(2,~1,~3\right) $ . | 1 |
3087 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~2,~3\right) $ and $ \vec{v_2} = \left(1,~-1,~1\right) $ . | 1 |
3088 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~3,~2\right) $ and $ \vec{v_2} = \left(-1,~2,~5\right) $ . | 1 |
3089 | Find the magnitude of the vector $ \| \vec{v} \| = \left(3,~0,~0\right) $ . | 1 |
3090 | Find the angle between vectors $ \left(2,~5\right)$ and $\left(-1,~3\right)$. | 1 |
3091 | Find the angle between vectors $ \left(4,~-1,~4\right)$ and $\left(3,~4,~-2\right)$. | 1 |
3092 | Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~-5\right) $ and $ \vec{v_2} = \left(-5,~4\right) $ . | 1 |
3093 | Calculate the dot product of the vectors $ \vec{v_1} = \left(4,~5,~-6\right) $ and $ \vec{v_2} = \left(2,~-3,~4\right) $ . | 1 |
3094 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-8,~-7\right) $ . | 1 |
3095 | Find the sum of the vectors $ \vec{v_1} = \left(-1,~3\right) $ and $ \vec{v_2} = \left(6,~2\right) $ . | 1 |
3096 | Find the angle between vectors $ \left(5,~-2,~4\right)$ and $\left(8,~3,~-2\right)$. | 1 |
3097 | Calculate the dot product of the vectors $ \vec{v_1} = \left(7,~-1\right) $ and $ \vec{v_2} = \left(4,~2\right) $ . | 1 |
3098 | Find the projection of the vector $ \vec{v_1} = \left(-9,~9,~9\right) $ on the vector $ \vec{v_2} = \left(6,~7,~6\right) $. | 1 |
3099 | Find the angle between vectors $ \left(1,~2,~3\right)$ and $\left(1,~2,~0\right)$. | 1 |
3100 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~0,~0\right) $ and $ \vec{v_2} = \left(0,~0,~0\right) $ . | 1 |