Vectors
(the database of solved problems)
All the problems and solutions shown below were generated using the Vectors Calculator.
| ID |
Problem |
Count |
| 2951 | Calculate the cross product of the vectors $ \vec{v_1} = \left(6,~-5,~1\right) $ and $ \vec{v_2} = \left(2,~1,~-4\right) $ . | 1 |
| 2952 | Calculate the cross product of the vectors $ \vec{v_1} = \left(6,~-5,~1\right) $ and $ \vec{v_2} = \left(6,~-5,~1\right) $ . | 1 |
| 2953 | Calculate the cross product of the vectors $ \vec{v_1} = \left(2,~1,~-4\right) $ and $ \vec{v_2} = \left(6,~-5,~1\right) $ . | 1 |
| 2954 | Calculate the cross product of the vectors $ \vec{v_1} = \left(8,~-4,~-3\right) $ and $ \vec{v_2} = \left(6,~-5,~1\right) $ . | 1 |
| 2955 | Calculate the cross product of the vectors $ \vec{v_1} = \left(8,~-4,~-3\right) $ and $ \vec{v_2} = \left(2,~1,~-4\right) $ . | 1 |
| 2956 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~2,~-4\right) $ and $ \vec{v_2} = \left(0,~5,~2\right) $ . | 1 |
| 2957 | Find the angle between vectors $ \left(5,~1,~0\right)$ and $\left(-11,~-11,~-8\right)$. | 1 |
| 2958 | Find the angle between vectors $ \left(-11,~-11,~-8\right)$ and $\left(-16,~-12,~-8\right)$. | 1 |
| 2959 | Find the angle between vectors $ \left(7,~2,~-2\right)$ and $\left(6,~-3,~0\right)$. | 1 |
| 2960 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~-1,~0\right) $ and $ \vec{v_2} = \left(1,~-1,~0\right) $ . | 1 |
| 2961 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~-1,~0\right) $ and $ \vec{v_2} = \left(0,~0,~1\right) $ . | 1 |
| 2962 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~0,~2\right) $ and $ \vec{v_2} = \left(1,~0,~2\right) $ . | 1 |
| 2963 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~0,~2\right) $ and $ \vec{v_2} = \left(0,~0,~1\right) $ . | 1 |
| 2964 | Calculate the dot product of the vectors $ \vec{v_1} = \left(0,~0,~1\right) $ and $ \vec{v_2} = \left(0,~0,~1\right) $ . | 1 |
| 2965 | Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~3,~1\right) $ and $ \vec{v_2} = \left(-1,~2,~4\right) $ . | 1 |
| 2966 | Calculate the cross product of the vectors $ \vec{v_1} = \left(0,~2,~0\right) $ and $ \vec{v_2} = \left(3,~0,~0\right) $ . | 1 |
| 2967 | Find the sum of the vectors $ \vec{v_1} = \left(2,~4,~0\right) $ and $ \vec{v_2} = \left(3,~0,~2\right) $ . | 1 |
| 2968 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-6,~4,~-4\right) $ and $ \vec{v_2} = \left(1,~-2,~-4\right) $ . | 1 |
| 2969 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-6,~-5,~-4\right) $ and $ \vec{v_2} = \left(6,~-6,~-4\right) $ . | 1 |
| 2970 | Find the projection of the vector $ \vec{v_1} = \left(-6,~-5,~-4\right) $ on the vector $ \vec{v_2} = \left(6,~-6,~-4\right) $. | 1 |
| 2971 | Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~4\right) $ and $ \vec{v_2} = \left(3,~9\right) $ . | 1 |
| 2972 | Calculate the dot product of the vectors $ \vec{v_1} = \left(5,~4\right) $ and $ \vec{v_2} = \left(8,~-10\right) $ . | 1 |
| 2973 | Find the angle between vectors $ \left(-3,~-5\right)$ and $\left(-15,~9\right)$. | 1 |
| 2974 | Find the angle between vectors $ \left(2,~4\right)$ and $\left(-1,~8\right)$. | 1 |
| 2975 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-6,~3,~-8\right) $ . | 1 |
| 2976 | Find the magnitude of the vector $ \| \vec{v} \| = \left(3,~5,~5\right) $ . | 1 |
| 2977 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-1,~3,~-7\right) $ . | 1 |
| 2978 | Find the sum of the vectors $ \vec{v_1} = \left(-3,~6\right) $ and $ \vec{v_2} = \left(-\dfrac{ 5 }{ 8 },~2\right) $ . | 1 |
| 2979 | Determine whether the vectors $ \vec{v_1} = \left(-8,~15\right) $ and $ \vec{v_2} = \left(0,~0\right) $ are linearly independent or dependent. | 1 |
| 2980 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-6,~-8\right) $ . | 1 |
| 2981 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-\dfrac{ 6321 }{ 5000 },~-0.0809,~-1\right) $ . | 1 |
| 2982 | Find the magnitude of the vector $ \| \vec{v} \| = \left(0,~1,~0\right) $ . | 1 |
| 2983 | Calculate the dot product of the vectors $ \vec{v_1} = \left(0,~1,~0\right) $ and $ \vec{v_2} = \left(-\dfrac{ 6321 }{ 5000 },~-0.0809,~-1\right) $ . | 1 |
| 2984 | Find the sum of the vectors $ \vec{v_1} = \left(0,~1,~0\right) $ and $ \vec{v_2} = \left(-\dfrac{ 6321 }{ 5000 },~-0.0809,~-1\right) $ . | 1 |
| 2985 | Find the magnitude of the vector $ \| \vec{v} \| = \left(4,~3\right) $ . | 1 |
| 2986 | Find the angle between vectors $ \left(0,~1,~0\right)$ and $\left(-\dfrac{ 6321 }{ 5000 },~-0.0809,~-1\right)$. | 1 |
| 2987 | Find the magnitude of the vector $ \| \vec{v} \| = \left(3,~4\right) $ . | 1 |
| 2988 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-\dfrac{ 6321 }{ 5000 },~-0.0809,~-1\right) $ . | 1 |
| 2989 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-\dfrac{ 6321 }{ 5000 },~-0.0809,~-1\right) $ and $ \vec{v_2} = \left(0,~1,~0\right) $ . | 1 |
| 2990 | Find the magnitude of the vector $ \| \vec{v} \| = \left(7,~-3\right) $ . | 1 |
| 2991 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-\dfrac{ 6879 }{ 5000 },~-0.192,~-1\right) $ and $ \vec{v_2} = \left(0,~1,~0\right) $ . | 1 |
| 2992 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-\dfrac{ 6879 }{ 5000 },~-0.192,~-1\right) $ and $ \vec{v_2} = \left(0,~1,~0\right) $ . | 1 |
| 2993 | Find the angle between vectors $ \left(-\dfrac{ 6879 }{ 5000 },~-0.192,~-1\right)$ and $\left(0,~1,~0\right)$. | 1 |
| 2994 | Find the magnitude of the vector $ \| \vec{v} \| = \left(2,~3\right) $ . | 1 |
| 2995 | Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~3\right) $ and $ \vec{v_2} = \left(-3,~-10\right) $ . | 1 |
| 2996 | Find the sum of the vectors $ \vec{v_1} = \left(2,~3\right) $ and $ \vec{v_2} = \left(-3,~-10\right) $ . | 1 |
| 2997 | Find the difference of the vectors $ \vec{v_1} = \left(2,~3\right) $ and $ \vec{v_2} = \left(-3,~-10\right) $ . | 1 |
| 2998 | Find the sum of the vectors $ \vec{v_1} = \left(-2,~-1\right) $ and $ \vec{v_2} = \left(3,~-2\right) $ . | 1 |
| 2999 | Find the difference of the vectors $ \vec{v_1} = \left(-2,~-1\right) $ and $ \vec{v_2} = \left(3,~-2\right) $ . | 1 |
| 3000 | Find the sum of the vectors $ \vec{v_1} = \left(1,~-2,~1\right) $ and $ \vec{v_2} = \left(2,~-1,~3\right) $ . | 1 |
