Vectors
(the database of solved problems)
All the problems and solutions shown below were generated using the Vectors Calculator.
| ID |
Problem |
Count |
| 2851 | Find the projection of the vector $ \vec{v_1} = \left(4,~-5\right) $ on the vector $ \vec{v_2} = \left(1,~9\right) $. | 1 |
| 2852 | Find the angle between vectors $ \left(4,~-5\right)$ and $\left(1,~9\right)$. | 1 |
| 2853 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~8,~3\right) $ and $ \vec{v_2} = \left(-2,~9,~1\right) $ . | 1 |
| 2854 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-7,~-6\right) $ . | 1 |
| 2855 | Find the magnitude of the vector $ \| \vec{v} \| = \left(4,~1,~2\right) $ . | 1 |
| 2856 | Find the projection of the vector $ \vec{v_1} = \left(4,~1,~2\right) $ on the vector $ \vec{v_2} = \left(3,~2,~4\right) $. | 1 |
| 2857 | Determine whether the vectors $ \vec{v_1} = \left(2,~1,~-2\right) $, $ \vec{v_2} = \left(1,~0,~0\right) $ and $ \vec{v_3} = \left(0,~0,~0\right)$ are linearly independent or dependent. | 1 |
| 2858 | Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~1,~-2\right) $ and $ \vec{v_2} = \left(1,~0,~0\right) $ . | 1 |
| 2859 | 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 |
| 2860 | Find the angle between vectors $ \left(3,~1,~2\right)$ and $\left(-1,~5,~-2\right)$. | 1 |
| 2861 | Find the magnitude of the vector $ \| \vec{v} \| = \left(3,~1,~2\right) $ . | 1 |
| 2862 | Find the projection of the vector $ \vec{v_1} = \left(3,~1,~2\right) $ on the vector $ \vec{v_2} = \left(-1,~5,~-2\right) $. | 1 |
| 2863 | Find the sum of the vectors $ \vec{v_1} = \left(3,~1,~2\right) $ and $ \vec{v_2} = \left(-1,~5,~-2\right) $ . | 1 |
| 2864 | Find the difference of the vectors $ \vec{v_1} = \left(3,~1,~2\right) $ and $ \vec{v_2} = \left(-1,~5,~-2\right) $ . | 1 |
| 2865 | Determine whether the vectors $ \vec{v_1} = \left(3,~1,~2\right) $, $ \vec{v_2} = \left(-1,~5,~-2\right) $ and $ \vec{v_3} = \left(0,~0,~0\right)$ are linearly independent or dependent. | 1 |
| 2866 | Find the difference of the vectors $ \vec{v_1} = \left(24,~40\right) $ and $ \vec{v_2} = \left(-20,~29\right) $ . | 1 |
| 2867 | Find the magnitude of the vector $ \| \vec{v} \| = \left(\sqrt{ 3 },~-1\right) $ . | 1 |
| 2868 | Find the projection of the vector $ \vec{v_1} = \left(\sqrt{ 3 },~3\right) $ on the vector $ \vec{v_2} = \left(1,~1\right) $. | 1 |
| 2869 | Calculate the dot product of the vectors $ \vec{v_1} = \left(\sqrt{ 3 },~-1\right) $ and $ \vec{v_2} = \left(-1,~1\right) $ . | 1 |
| 2870 | Find the angle between vectors $ \left(3806.5,~1774.9\right)$ and $\left(2544.1,~-1589.7\right)$. | 1 |
| 2871 | 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 |
| 2872 | Find the angle between vectors $ \left(0,~40\right)$ and $\left(20,~0\right)$. | 1 |
| 2873 | Find the magnitude of the vector $ \| \vec{v} \| = \left(7.07,~7.07\right) $ . | 1 |
| 2874 | Determine whether the vectors $ \vec{v_1} = \left(2,~0\right) $ and $ \vec{v_2} = \left(-3,~-5\right) $ are linearly independent or dependent. | 1 |
| 2875 | Determine whether the vectors $ \vec{v_1} = \left(-4,~-2\right) $ and $ \vec{v_2} = \left(5,~4\right) $ are linearly independent or dependent. | 1 |
| 2876 | Find the sum of the vectors $ \vec{v_1} = \left(-4,~\dfrac{ 1 }{ 4 }\right) $ and $ \vec{v_2} = \left(2,~-\dfrac{ 1 }{ 8 }\right) $ . | 1 |
| 2877 | Find the sum of the vectors $ \vec{v_1} = \left(-\dfrac{ 1 }{ 5 },~\dfrac{ 3 }{ 5 }\right) $ and $ \vec{v_2} = \left(1,~-\dfrac{ 1 }{ 5 }\right) $ . | 1 |
| 2878 | Find the angle between vectors $ \left(6,~11\right)$ and $\left(3,~-4\right)$. | 1 |
| 2879 | Find the angle between vectors $ \left(-12,~-4\right)$ and $\left(7,~10\right)$. | 1 |
| 2880 | Find the sum of the vectors $ \vec{v_1} = \left(\dfrac{ 3 }{ 5 },~-\dfrac{ 3 }{ 5 }\right) $ and $ \vec{v_2} = \left(\dfrac{ 4 }{ 5 },~\dfrac{ 3 }{ 5 }\right) $ . | 1 |
| 2881 | Find the difference of the vectors $ \vec{v_1} = \left(-5,~5\right) $ and $ \vec{v_2} = \left(3,~6\right) $ . | 1 |
| 2882 | Find the angle between vectors $ \left(-5,~5\right)$ and $\left(3,~6\right)$. | 1 |
| 2883 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-5,~5\right) $ . | 1 |
| 2884 | Find the angle between vectors $ \left(-5,~5\right)$ and $\left(4,~-7\right)$. | 1 |
| 2885 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-5,~5\right) $ . | 1 |
| 2886 | Find the sum of the vectors $ \vec{v_1} = \left(\dfrac{ 3 }{ 5 },~-\dfrac{ 4 }{ 5 }\right) $ and $ \vec{v_2} = \left(\dfrac{ 4 }{ 5 },~\dfrac{ 2 }{ 5 }\right) $ . | 1 |
| 2887 | Find the magnitude of the vector $ \| \vec{v} \| = \left(\dfrac{ 9 }{ 2 },~-6\right) $ . | 1 |
| 2888 | Find the magnitude of the vector $ \| \vec{v} \| = \left(7,~-11\right) $ . | 1 |
| 2889 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-8,~8\right) $ . | 1 |
| 2890 | Find the sum of the vectors $ \vec{v_1} = \left(1,~2\right) $ and $ \vec{v_2} = \left(3,~2\right) $ . | 1 |
| 2891 | Find the magnitude of the vector $ \| \vec{v} \| = \left(\dfrac{ 8119 }{ 3125 },~\dfrac{ 3 }{ 2 }\right) $ . | 1 |
| 2892 | Find the sum of the vectors $ \vec{v_1} = \left(6,~-3\right) $ and $ \vec{v_2} = \left(-4,~1\right) $ . | 1 |
| 2893 | Find the difference of the vectors $ \vec{v_1} = \left(2,~1\right) $ and $ \vec{v_2} = \left(4,~-1\right) $ . | 1 |
| 2894 | Find the magnitude of the vector $ \| \vec{v} \| = \left(1,~-2\right) $ . | 1 |
| 2895 | Calculate the dot product of the vectors $ \vec{v_1} = \left(6,~-2\right) $ and $ \vec{v_2} = \left(-4,~-1\right) $ . | 1 |
| 2896 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-3,~1,~5\right) $ . | 1 |
| 2897 | 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 |
| 2898 | Find the sum of the vectors $ \vec{v_1} = \left(8,~3\right) $ and $ \vec{v_2} = \left(1,~7\right) $ . | 1 |
| 2899 | Find the magnitude of the vector $ \| \vec{v} \| = \left(210,~180\right) $ . | 1 |
| 2900 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-6,~-5\right) $ . | 1 |
