Vectors – Solved Problems Database
All the problems and solutions shown below were generated using the Vectors Calculator.
ID |
Problem |
Count |
901 | Find the sum of the vectors $ \vec{v_1} = \left(1,~2\right) $ and $ \vec{v_2} = \left(2,~2\right) $ . | 2 |
902 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-3,~-5\right) $ . | 2 |
903 | Find the angle between vectors $ \left(4,~-5\right)$ and $\left(8,~-1\right)$. | 2 |
904 | Find the difference of the vectors $ \vec{v_1} = \left(230,~30\right) $ and $ \vec{v_2} = \left(-150,~309.23\right) $ . | 2 |
905 | Find the magnitude of the vector $ \| \vec{v} \| = \left(8,~-4\right) $ . | 2 |
906 | Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~7\right) $ and $ \vec{v_2} = \left(7,~1\right) $ . | 2 |
907 | Find the projection of the vector $ \vec{v_1} = \left(5,~12\right) $ on the vector $ \vec{v_2} = \left(-4,~3\right) $. | 2 |
908 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-\dfrac{ 81 }{ 1000 },~-\dfrac{ 327 }{ 500 }\right) $ . | 2 |
909 | Find the magnitude of the vector $ \| \vec{v} \| = \left(3,~3\right) $ . | 2 |
910 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-1,~2\right) $ and $ \vec{v_2} = \left(-2,~0\right) $ . | 2 |
911 | Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~4\right) $ and $ \vec{v_2} = \left(15,~-15\right) $ . | 2 |
912 | Find the magnitude of the vector $ \| \vec{v} \| = \left(20,~0\right) $ . | 2 |
913 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-1,~5\right) $ . | 2 |
914 | Determine whether the vectors $ \vec{v_1} = \left(-\dfrac{ 27 }{ 100 },~-\dfrac{ 9 }{ 25 }\right) $ and $ \vec{v_2} = \left(-\dfrac{ 27 }{ 100 },~-\dfrac{ 9 }{ 25 }\right) $ are linearly independent or dependent. | 2 |
915 | Find the sum of the vectors $ \vec{v_1} = \left(2,~-5\right) $ and $ \vec{v_2} = \left(4,~7\right) $ . | 2 |
916 | Find the magnitude of the vector $ \| \vec{v} \| = \left(4,~5\right) $ . | 2 |
917 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-7,~24\right) $ . | 2 |
918 | Find the sum of the vectors $ \vec{v_1} = \left(6,~-2\right) $ and $ \vec{v_2} = \left(-3,~-5\right) $ . | 2 |
919 | Find the magnitude of the vector $ \| \vec{v} \| = \left(7,~8\right) $ . | 2 |
920 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~1,~1\right) $ and $ \vec{v_2} = \left(1,~2,~1\right) $ . | 2 |
921 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-8,~8\right) $ and $ \vec{v_2} = \left(1,~1\right) $ . | 2 |
922 | Determine whether the vectors $ \vec{v_1} = \left(4,~4,~4\right) $, $ \vec{v_2} = \left(11,~11,~11\right) $ and $ \vec{v_3} = \left(0,~0,~0\right)$ are linearly independent or dependent. | 2 |
923 | Calculate the dot product of the vectors $ \vec{v_1} = \left(4,~2\right) $ and $ \vec{v_2} = \left(-2,~4\right) $ . | 2 |
924 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-6,~6\right) $ . | 2 |
925 | Find the magnitude of the vector $ \| \vec{v} \| = \left(0,~0\right) $ . | 2 |
926 | Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~8\right) $ and $ \vec{v_2} = \left(-8,~-2\right) $ . | 2 |
927 | Find the magnitude of the vector $ \| \vec{v} \| = \left(2,~-2,~1\right) $ . | 2 |
928 | Determine whether the vectors $ \vec{v_1} = \left(4,~5\right) $ and $ \vec{v_2} = \left(-5,~11\right) $ are linearly independent or dependent. | 2 |
929 | Calculate the cross product of the vectors $ \vec{v_1} = \left(2,~3,~0\right) $ and $ \vec{v_2} = \left(1,~0,~7\right) $ . | 2 |
930 | Find the magnitude of the vector $ \| \vec{v} \| = \left(8,~-1\right) $ . | 2 |
931 | Find the sum of the vectors $ \vec{v_1} = \left(2,~1\right) $ and $ \vec{v_2} = \left(-24,~-6\right) $ . | 2 |
932 | Find the angle between vectors $ \left(-8,~8\right)$ and $\left(1,~1\right)$. | 2 |
933 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-3,~-1\right) $ and $ \vec{v_2} = \left(-9,~-2\right) $ . | 2 |
934 | Find the angle between vectors $ \left(4,~2\right)$ and $\left(-2,~4\right)$. | 2 |
935 | Find the difference of the vectors $ \vec{v_1} = \left(6,~2\right) $ and $ \vec{v_2} = \left(11,~-4\right) $ . | 2 |
936 | Find the sum of the vectors $ \vec{v_1} = \left(7,~9\right) $ and $ \vec{v_2} = \left(4,~6\right) $ . | 2 |
937 | Calculate the cross product of the vectors $ \vec{v_1} = \left(2,~-1,~1\right) $ and $ \vec{v_2} = \left(10,~-12,~5\right) $ . | 2 |
938 | Find the difference of the vectors $ \vec{v_1} = \left(250,~110\right) $ and $ \vec{v_2} = \left(-200,~0\right) $ . | 2 |
939 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-8,~8\right) $ and $ \vec{v_2} = \left(1,~-1\right) $ . | 2 |
940 | Find the difference of the vectors $ \vec{v_1} = \left(4,~-2\right) $ and $ \vec{v_2} = \left(-3,~5\right) $ . | 2 |
941 | Find the sum of the vectors $ \vec{v_1} = \left(5,~-8\right) $ and $ \vec{v_2} = \left(1,~-7\right) $ . | 2 |
942 | Find the difference of the vectors $ \vec{v_1} = \left(4,~-7\right) $ and $ \vec{v_2} = \left(2,~3\right) $ . | 2 |
943 | Calculate the cross product of the vectors $ \vec{v_1} = \left(2,~-1,~1\right) $ and $ \vec{v_2} = \left(6,~-4,~3\right) $ . | 2 |
944 | Find the magnitude of the vector $ \| \vec{v} \| = \left(9,~12\right) $ . | 2 |
945 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-5,~-4\right) $ and $ \vec{v_2} = \left(-2,~\dfrac{ 1 }{ 4 }\right) $ . | 2 |
946 | Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~2\right) $ and $ \vec{v_2} = \left(4,~5\right) $ . | 2 |
947 | Find the magnitude of the vector $ \| \vec{v} \| = \left(3,~-7\right) $ . | 2 |
948 | Find the magnitude of the vector $ \| \vec{v} \| = \left(2,~1\right) $ . | 2 |
949 | Find the angle between vectors $ \left(-1,~-3\right)$ and $\left(-2,~-3\right)$. | 2 |
950 | Find the angle between vectors $ \left(-8,~8\right)$ and $\left(1,~-1\right)$. | 2 |