Vectors – Solved Problems Database
All the problems and solutions shown below were generated using the Vectors Calculator.
ID |
Problem |
Count |
801 | Determine whether the vectors $ \vec{v_1} = \left(1,~3\right) $ and $ \vec{v_2} = \left(1,~4\right) $ are linearly independent or dependent. | 2 |
802 | Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~3\right) $ and $ \vec{v_2} = \left(-1,~-2\right) $ . | 2 |
803 | Find the magnitude of the vector $ \| \vec{v} \| = \left(8,~6\right) $ . | 2 |
804 | Find the sum of the vectors $ \vec{v_1} = \left(-20,~-25\right) $ and $ \vec{v_2} = \left(4,~-4\right) $ . | 2 |
805 | Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~3\right) $ and $ \vec{v_2} = \left(3,~2\right) $ . | 2 |
806 | Find the magnitude of the vector $ \| \vec{v} \| = \left(8,~5\right) $ . | 2 |
807 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-3,~2\right) $ . | 2 |
808 | Find the difference of the vectors $ \vec{v_1} = \left(30,~24\right) $ and $ \vec{v_2} = \left(54,~18\right) $ . | 2 |
809 | Calculate the dot product of the vectors $ \vec{v_1} = \left(0,~-5,~-3\right) $ and $ \vec{v_2} = \left(0,~-5,~-5\right) $ . | 2 |
810 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-7,~5\right) $ and $ \vec{v_2} = \left(6,~5\right) $ . | 2 |
811 | Calculate the dot product of the vectors $ \vec{v_1} = \left(8,~6\right) $ and $ \vec{v_2} = \left(-3,~4\right) $ . | 2 |
812 | Find the sum of the vectors $ \vec{v_1} = \left(1,~2\right) $ and $ \vec{v_2} = \left(1,~2\right) $ . | 2 |
813 | Calculate the dot product of the vectors $ \vec{v_1} = \left(8,~5\right) $ and $ \vec{v_2} = \left(5,~-8\right) $ . | 2 |
814 | Find the magnitude of the vector $ \| \vec{v} \| = \left(3130,~108\right) $ . | 2 |
815 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-7,~2\right) $ and $ \vec{v_2} = \left(-1,~-3\right) $ . | 2 |
816 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-7,~5\right) $ and $ \vec{v_2} = \left(6,~6\right) $ . | 2 |
817 | Calculate the cross product of the vectors $ \vec{v_1} = \left(3,~0,~4\right) $ and $ \vec{v_2} = \left(-2,~2,~1\right) $ . | 2 |
818 | Find the sum of the vectors $ \vec{v_1} = \left(-1,~-4,~2\right) $ and $ \vec{v_2} = \left(3,~3,~-2\right) $ . | 2 |
819 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-5,~0\right) $ . | 2 |
820 | Find the sum of the vectors $ \vec{v_1} = \left(1,~9\right) $ and $ \vec{v_2} = \left(4,~3\right) $ . | 2 |
821 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-2,~7\right) $ and $ \vec{v_2} = \left(-5,~-8\right) $ . | 2 |
822 | Find the sum of the vectors $ \vec{v_1} = \left(14,~-10\right) $ and $ \vec{v_2} = \left(9,~-4\right) $ . | 2 |
823 | Find the angle between vectors $ \left(-3,~-2\right)$ and $\left(5,~-7\right)$. | 2 |
824 | Find the projection of the vector $ \vec{v_1} = \left(3,~9\right) $ on the vector $ \vec{v_2} = \left(6,~-3\right) $. | 2 |
825 | Find the difference of the vectors $ \vec{v_1} = \left(-3,~4\right) $ and $ \vec{v_2} = \left(-2,~7\right) $ . | 2 |
826 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-7,~5\right) $ and $ \vec{v_2} = \left(6,~7\right) $ . | 2 |
827 | Find the magnitude of the vector $ \| \vec{v} \| = \left(0,~0\right) $ . | 2 |
828 | Calculate the cross product of the vectors $ \vec{v_1} = \left(3,~0,~2\right) $ and $ \vec{v_2} = \left(0,~3,~1\right) $ . | 2 |
829 | Find the sum of the vectors $ \vec{v_1} = \left(\dfrac{ 14 }{ 5 },~-1\right) $ and $ \vec{v_2} = \left(0,~2\right) $ . | 2 |
830 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-5,~-1\right) $ . | 2 |
831 | Determine whether the vectors $ \vec{v_1} = \left(-3,~1\right) $ and $ \vec{v_2} = \left(8,~-6\right) $ are linearly independent or dependent. | 2 |
832 | Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~6\right) $ and $ \vec{v_2} = \left(7,~35\right) $ . | 2 |
833 | Find the magnitude of the vector $ \| \vec{v} \| = \left(\dfrac{ 24 }{ 5 },~-4\right) $ . | 2 |
834 | Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~2,~1\right) $ and $ \vec{v_2} = \left(2,~-1,~0\right) $ . | 2 |
835 | Calculate the dot product of the vectors $ \vec{v_1} = \left(0,~0\right) $ and $ \vec{v_2} = \left(1,~1\right) $ . | 2 |
836 | Find the sum of the vectors $ \vec{v_1} = \left(-5,~6\right) $ and $ \vec{v_2} = \left(8,~-4\right) $ . | 2 |
837 | Find the magnitude of the vector $ \| \vec{v} \| = \left(1,~-3\right) $ . | 2 |
838 | Find the sum of the vectors $ \vec{v_1} = \left(\dfrac{ 14 }{ 5 },~1\right) $ and $ \vec{v_2} = \left(-\dfrac{ 17 }{ 10 },~-\dfrac{ 47 }{ 10 }\right) $ . | 2 |
839 | Calculate the dot product of the vectors $ \vec{v_1} = \left(7,~4\right) $ and $ \vec{v_2} = \left(-6,~2\right) $ . | 2 |
840 | Find the angle between vectors $ \left(0,~1\right)$ and $\left(1,~1\right)$. | 2 |
841 | Find the difference of the vectors $ \vec{v_1} = \left(-2,~4\right) $ and $ \vec{v_2} = \left(5,~-4\right) $ . | 2 |
842 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~4\right) $ and $ \vec{v_2} = \left(1,~4\right) $ . | 2 |
843 | Find the difference of the vectors $ \vec{v_1} = \left(240,~20\right) $ and $ \vec{v_2} = \left(-150,~309.23\right) $ . | 2 |
844 | Find the magnitude of the vector $ \| \vec{v} \| = \left(2,~3\right) $ . | 2 |
845 | Determine whether the vectors $ \vec{v_1} = \left(0,~1\right) $ and $ \vec{v_2} = \left(1,~1\right) $ are linearly independent or dependent. | 2 |
846 | Find the magnitude of the vector $ \| \vec{v} \| = \left(0,~0,~1\right) $ . | 2 |
847 | Find the sum of the vectors $ \vec{v_1} = \left(8,~2\right) $ and $ \vec{v_2} = \left(-6,~8\right) $ . | 2 |
848 | Find the sum of the vectors $ \vec{v_1} = \left(-5,~2\right) $ and $ \vec{v_2} = \left(2,~-3\right) $ . | 2 |
849 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~2\right) $ and $ \vec{v_2} = \left(\dfrac{ 1 }{ 2 },~-\dfrac{ 1 }{ 2 }\right) $ . | 2 |
850 | Find the sum of the vectors $ \vec{v_1} = \left(-5,~-1\right) $ and $ \vec{v_2} = \left(3,~2\right) $ . | 2 |