Vectors – Solved Problems Database
All the problems and solutions shown below were generated using the Vectors Calculator.
ID |
Problem |
Count |
851 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-7,~5\right) $ and $ \vec{v_2} = \left(6,~9\right) $ . | 2 |
852 | Determine whether the vectors $ \vec{v_1} = \left(3,~5\right) $ and $ \vec{v_2} = \left(2,~4\right) $ are linearly independent or dependent. | 2 |
853 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-3,~-2\right) $ . | 2 |
854 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~2,~3\right) $ and $ \vec{v_2} = \left(4,~5,~6\right) $ . | 2 |
855 | Calculate the cross product of the vectors $ \vec{v_1} = \left(3,~-3,~1\right) $ and $ \vec{v_2} = \left(4,~9,~2\right) $ . | 2 |
856 | Find the sum of the vectors $ \vec{v_1} = \left(-2,~58\right) $ and $ \vec{v_2} = \left(3,~17\right) $ . | 2 |
857 | Find the sum of the vectors $ \vec{v_1} = \left(5,~-2\right) $ and $ \vec{v_2} = \left(-2,~3\right) $ . | 2 |
858 | Find the magnitude of the vector $ \| \vec{v} \| = \left(10,~0\right) $ . | 2 |
859 | Calculate the dot product of the vectors $ \vec{v_1} = \left(7,~-3\right) $ and $ \vec{v_2} = \left(7,~-3\right) $ . | 2 |
860 | Find the magnitude of the vector $ \| \vec{v} \| = \left(6,~4\right) $ . | 2 |
861 | Find the angle between vectors $ \left(7,~5\right)$ and $\left(9,~0\right)$. | 2 |
862 | Find the sum of the vectors $ \vec{v_1} = \left(-2,~6\right) $ and $ \vec{v_2} = \left(12,~-18\right) $ . | 2 |
863 | Find the projection of the vector $ \vec{v_1} = \left(0,~1\right) $ on the vector $ \vec{v_2} = \left(1,~1\right) $. | 2 |
864 | Find the angle between vectors $ \left(3,~4\right)$ and $\left(6,~8\right)$. | 2 |
865 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-3,~-1\right) $ . | 2 |
866 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~1,~1\right) $ and $ \vec{v_2} = \left(1,~1,~1\right) $ . | 2 |
867 | Find the sum of the vectors $ \vec{v_1} = \left(-10,~5\right) $ and $ \vec{v_2} = \left(-9,~-10\right) $ . | 2 |
868 | Find the magnitude of the vector $ \| \vec{v} \| = \left(3130,~108\right) $ . | 2 |
869 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-24,~7\right) $ . | 2 |
870 | Calculate the dot product of the vectors $ \vec{v_1} = \left(\dfrac{ 4 }{ 5 },~-\dfrac{ 8 }{ 5 }\right) $ and $ \vec{v_2} = \left(4,~2\right) $ . | 2 |
871 | Find the magnitude of the vector $ \| \vec{v} \| = \left(1,~2\right) $ . | 2 |
872 | Find the difference of the vectors $ \vec{v_1} = \left(2,~7\right) $ and $ \vec{v_2} = \left(5,~2\right) $ . | 2 |
873 | Find the sum of the vectors $ \vec{v_1} = \left(5,~8\right) $ and $ \vec{v_2} = \left(-9,~2\right) $ . | 2 |
874 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-7,~-3\right) $ and $ \vec{v_2} = \left(-10,~-5\right) $ . | 2 |
875 | Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~-3\right) $ and $ \vec{v_2} = \left(-1,~3\right) $ . | 2 |
876 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~-3\right) $ and $ \vec{v_2} = \left(-2,~6\right) $ . | 2 |
877 | Find the magnitude of the vector $ \| \vec{v} \| = \left(6,~-3\right) $ . | 2 |
878 | Calculate the cross product of the vectors $ \vec{v_1} = \left(2,~3,~-4\right) $ and $ \vec{v_2} = \left(-3,~2,~3\right) $ . | 2 |
879 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-7,~-3\right) $ and $ \vec{v_2} = \left(-7,~-3\right) $ . | 2 |
880 | Calculate the dot product of the vectors $ \vec{v_1} = \left(4,~-24\right) $ and $ \vec{v_2} = \left(6,~1\right) $ . | 2 |
881 | Find the difference of the vectors $ \vec{v_1} = \left(-3,~-6\right) $ and $ \vec{v_2} = \left(-4,~-9\right) $ . | 2 |
882 | Find the angle between vectors $ \left(-4,~3\right)$ and $\left(5,~12\right)$. | 2 |
883 | Find the magnitude of the vector $ \| \vec{v} \| = \left(184,~47\right) $ . | 2 |
884 | Find the angle between vectors $ \left(-2,~1\right)$ and $\left(-1,~-4\right)$. | 2 |
885 | Calculate the dot product of the vectors $ \vec{v_1} = \left(12,~5\right) $ and $ \vec{v_2} = \left(2,~8\right) $ . | 2 |
886 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-4,~4\right) $ . | 2 |
887 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~1,~0\right) $ and $ \vec{v_2} = \left(-1,~1,~2\right) $ . | 2 |
888 | Find the sum of the vectors $ \vec{v_1} = \left(0,~34\right) $ and $ \vec{v_2} = \left(34,~0\right) $ . | 2 |
889 | Find the sum of the vectors $ \vec{v_1} = \left(-7,~-3\right) $ and $ \vec{v_2} = \left(-5,~7\right) $ . | 2 |
890 | Find the angle between vectors $ \left(2,~0\right)$ and $\left(1,~3\right)$. | 2 |
891 | Determine whether the vectors $ \vec{v_1} = \left(3,~4\right) $ and $ \vec{v_2} = \left(6,~8\right) $ are linearly independent or dependent. | 2 |
892 | Calculate the dot product of the vectors $ \vec{v_1} = \left(8,~2\right) $ and $ \vec{v_2} = \left(-6,~8\right) $ . | 2 |
893 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-4,~3,~2\right) $ . | 2 |
894 | Find the angle between vectors $ \left(5,~-1\right)$ and $\left(2,~3\right)$. | 2 |
895 | Find the angle between vectors $ \left(2,~-1\right)$ and $\left(-5,~-4\right)$. | 2 |
896 | Find the sum of the vectors $ \vec{v_1} = \left(184,~47\right) $ and $ \vec{v_2} = \left(44,~44\right) $ . | 2 |
897 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-2,~6\right) $ and $ \vec{v_2} = \left(-3,~8\right) $ . | 2 |
898 | Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~1\right) $ and $ \vec{v_2} = \left(2,~2\right) $ . | 2 |
899 | Find the difference of the vectors $ \vec{v_1} = \left(\dfrac{ 8119 }{ 3125 },~\dfrac{ 3 }{ 2 }\right) $ and $ \vec{v_2} = \left(-5,~0\right) $ . | 2 |
900 | Find the sum of the vectors $ \vec{v_1} = \left(-2,~4\right) $ and $ \vec{v_2} = \left(7,~-1\right) $ . | 2 |