Vectors
(the database of solved problems)
All the problems and solutions shown below were generated using the Vectors Calculator.
| ID |
Problem |
Count |
| 2901 | Find the magnitude of the vector $ \| \vec{v} \| = \left(6,~30\right) $ . | 1 |
| 2902 | Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~-3,~1\right) $ and $ \vec{v_2} = \left(-4,~-1,~2\right) $ . | 1 |
| 2903 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-2,~1\right) $ . | 1 |
| 2904 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-5,~-5\right) $ . | 1 |
| 2905 | Find the magnitude of the vector $ \| \vec{v} \| = \left(1,~-3\right) $ . | 1 |
| 2906 | Find the magnitude of the vector $ \| \vec{v} \| = \left(1,~2,~3\right) $ . | 1 |
| 2907 | Find the magnitude of the vector $ \| \vec{v} \| = \left(4,~-5,~6\right) $ . | 1 |
| 2908 | Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~-5\right) $ and $ \vec{v_2} = \left(6,~-10\right) $ . | 1 |
| 2909 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-1,~-2\right) $ and $ \vec{v_2} = \left(0,~2\right) $ . | 1 |
| 2910 | Find the difference of the vectors $ \vec{v_1} = \left(0,~-1,~-3\right) $ and $ \vec{v_2} = \left(1,~2,~-5\right) $ . | 1 |
| 2911 | Find the difference of the vectors $ \vec{v_1} = \left(1,~2,~-5\right) $ and $ \vec{v_2} = \left(0,~-1,~-3\right) $ . | 1 |
| 2912 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-1,~5\right) $ . | 1 |
| 2913 | Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~-1,~3\right) $ and $ \vec{v_2} = \left(1,~-2,~-4\right) $ . | 1 |
| 2914 | Calculate the dot product of the vectors $ \vec{v_1} = \left(4,~2,~-3\right) $ and $ \vec{v_2} = \left(3,~-1,~-1\right) $ . | 1 |
| 2915 | Find the angle between vectors $ \left(4,~2,~-3\right)$ and $\left(3,~-1,~-1\right)$. | 1 |
| 2916 | 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 |
| 2917 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-3,~-3 \sqrt{ 3 }\right) $ . | 1 |
| 2918 | Calculate the dot product of the vectors $ \vec{v_1} = \left(12,~4\right) $ and $ \vec{v_2} = \left(3,~9\right) $ . | 1 |
| 2919 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-5,~2\right) $ . | 1 |
| 2920 | Find the sum of the vectors $ \vec{v_1} = \left(4,~-3\right) $ and $ \vec{v_2} = \left(-2,~1\right) $ . | 1 |
| 2921 | Find the magnitude of the vector $ \| \vec{v} \| = \left(\dfrac{ 1 }{ 9 },~\dfrac{ 8 }{ 9 }\right) $ . | 1 |
| 2922 | Determine whether the vectors $ \vec{v_1} = \left(4,~6,~2\right) $, $ \vec{v_2} = \left(2,~3,~0\right) $ and $ \vec{v_3} = \left(2,~3,~2\right)$ are linearly independent or dependent. | 1 |
| 2923 | Find the magnitude of the vector $ \| \vec{v} \| = \left(4,~-5\right) $ . | 1 |
| 2924 | Find the sum of the vectors $ \vec{v_1} = \left(0,~5\right) $ and $ \vec{v_2} = \left(-7,~0\right) $ . | 1 |
| 2925 | Determine whether the vectors $ \vec{v_1} = \left(4,~6,~2\right) $, $ \vec{v_2} = \left(2,~3,~0\right) $ and $ \vec{v_3} = \left(0,~0,~0\right)$ are linearly independent or dependent. | 1 |
| 2926 | Calculate the cross product of the vectors $ \vec{v_1} = \left(2,~3,~4\right) $ and $ \vec{v_2} = \left(5,~6,~7\right) $ . | 1 |
| 2927 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-2,~3,~5\right) $ and $ \vec{v_2} = \left(-4,~6,~1\right) $ . | 1 |
| 2928 | Calculate the dot product of the vectors $ \vec{v_1} = \left(4,~6,~2\right) $ and $ \vec{v_2} = \left(2,~3,~0\right) $ . | 1 |
| 2929 | Calculate the cross product of the vectors $ \vec{v_1} = \left(3,~-3,~1\right) $ and $ \vec{v_2} = \left(-12,~12,~-4\right) $ . | 1 |
| 2930 | Calculate the cross product of the vectors $ \vec{v_1} = \left(0,~2,~-5\right) $ and $ \vec{v_2} = \left(1,~1,~2\right) $ . | 1 |
| 2931 | Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~1,~-3\right) $ and $ \vec{v_2} = \left(9,~-5,~-2\right) $ . | 1 |
| 2932 | Calculate the cross product of the vectors $ \vec{v_1} = \left(0,~4,~0\right) $ and $ \vec{v_2} = \left(-1,~3,~3\right) $ . | 1 |
| 2933 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-2,~3,~1\right) $ and $ \vec{v_2} = \left(12,~0,~4\right) $ . | 1 |
| 2934 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~1,~-1\right) $ and $ \vec{v_2} = \left(-2,~7,~3\right) $ . | 1 |
| 2935 | Find the angle between vectors $ \left(-7,~-1\right)$ and $\left(-4,~-6\right)$. | 1 |
| 2936 | Find the angle between vectors $ \left(4,~2,~-3\right)$ and $\left(1,~-3,~-1\right)$. | 1 |
| 2937 | Find the projection of the vector $ \vec{v_1} = \left(4,~2,~-3\right) $ on the vector $ \vec{v_2} = \left(1,~-3,~-1\right) $. | 1 |
| 2938 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-5,~3,~-1\right) $ . | 1 |
| 2939 | Find the angle between vectors $ \left(-3,~-5,~-2\right)$ and $\left(2,~-1,~-5\right)$. | 1 |
| 2940 | Find the angle between vectors $ \left(1,~3,~2\right)$ and $\left(3,~4,~2\right)$. | 1 |
| 2941 | Find the projection of the vector $ \vec{v_1} = \left(-1,~5\right) $ on the vector $ \vec{v_2} = \left(-5,~5\right) $. | 1 |
| 2942 | Find the projection of the vector $ \vec{v_1} = \left(-5,~5\right) $ on the vector $ \vec{v_2} = \left(-1,~5\right) $. | 1 |
| 2943 | Find the projection of the vector $ \vec{v_1} = \left(1,~5,~-1\right) $ on the vector $ \vec{v_2} = \left(2,~0,~4\right) $. | 1 |
| 2944 | Find the projection of the vector $ \vec{v_1} = \left(1,~-2\right) $ on the vector $ \vec{v_2} = \left(-4,~10\right) $. | 1 |
| 2945 | Find the projection of the vector $ \vec{v_1} = \left(-4,~10\right) $ on the vector $ \vec{v_2} = \left(1,~-2\right) $. | 1 |
| 2946 | Find the projection of the vector $ \vec{v_1} = \left(8,~1\right) $ on the vector $ \vec{v_2} = \left(-8,~4\right) $. | 1 |
| 2947 | Find the projection of the vector $ \vec{v_1} = \left(-5,~9,~2\right) $ on the vector $ \vec{v_2} = \left(3,~-2,~5\right) $. | 1 |
| 2948 | Calculate the cross product of the vectors $ \vec{v_1} = \left(3,~5,~0\right) $ and $ \vec{v_2} = \left(-3,~-1,~0\right) $ . | 1 |
| 2949 | Calculate the cross product of the vectors $ \vec{v_1} = \left(6,~-5,~2\right) $ and $ \vec{v_2} = \left(-3,~-8,~8\right) $ . | 1 |
| 2950 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-3,~-10,~2\right) $ and $ \vec{v_2} = \left(7,~2,~8\right) $ . | 1 |
