Vectors – Solved Problems Database
All the problems and solutions shown below were generated using the Vectors Calculator.
ID |
Problem |
Count |
701 | Find the magnitude of the vector $ \| \vec{v} \| = \left(0,~0\right) $ . | 2 |
702 | Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~4\right) $ and $ \vec{v_2} = \left(8,~2\right) $ . | 2 |
703 | Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~4\right) $ and $ \vec{v_2} = \left(2,~8\right) $ . | 2 |
704 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-3,~7\right) $ . | 2 |
705 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-1,~-4\right) $ . | 2 |
706 | Find the magnitude of the vector $ \| \vec{v} \| = \left(3,~8\right) $ . | 2 |
707 | Find the difference of the vectors $ \vec{v_1} = \left(5,~7\right) $ and $ \vec{v_2} = \left(-1,~1\right) $ . | 2 |
708 | Calculate the dot product of the vectors $ \vec{v_1} = \left(0,~0\right) $ and $ \vec{v_2} = \left(0,~0\right) $ . | 2 |
709 | Find the projection of the vector $ \vec{v_1} = \left(-19,~-9,~16\right) $ on the vector $ \vec{v_2} = \left(-6,~-2,~6\right) $. | 2 |
710 | Calculate the dot product of the vectors $ \vec{v_1} = \left(\dfrac{ 8 }{ 17 },~\dfrac{ 8 }{ 17 }\right) $ and $ \vec{v_2} = \left(8,~2\right) $ . | 2 |
711 | Calculate the dot product of the vectors $ \vec{v_1} = \left(4,~5\right) $ and $ \vec{v_2} = \left(-4,~8\right) $ . | 2 |
712 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-8,~\sqrt{ 7 }\right) $ . | 2 |
713 | Find the angle between vectors $ \left(9,~6\right)$ and $\left(-4,~5\right)$. | 2 |
714 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-7,~-24\right) $ . | 2 |
715 | Find the difference of the vectors $ \vec{v_1} = \left(-4,~-1\right) $ and $ \vec{v_2} = \left(4,~2\right) $ . | 2 |
716 | Find the magnitude of the vector $ \| \vec{v} \| = \left(5,~7\right) $ . | 2 |
717 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-20,~-25\right) $ and $ \vec{v_2} = \left(4,~-4\right) $ . | 2 |
718 | Find the magnitude of the vector $ \| \vec{v} \| = \left(1,~0\right) $ . | 2 |
719 | Find the angle between vectors $ \left(3,~4\right)$ and $\left(2,~8\right)$. | 2 |
720 | Find the magnitude of the vector $ \| \vec{v} \| = \left(5,~2\right) $ . | 2 |
721 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-4,~-3\right) $ . | 2 |
722 | Find the magnitude of the vector $ \| \vec{v} \| = \left(4,~5\right) $ . | 2 |
723 | Find the sum of the vectors $ \vec{v_1} = \left(2,~1\right) $ and $ \vec{v_2} = \left(1,~2\right) $ . | 2 |
724 | Calculate the dot product of the vectors $ \vec{v_1} = \left(5,~7\right) $ and $ \vec{v_2} = \left(-1,~1\right) $ . | 2 |
725 | Find the sum of the vectors $ \vec{v_1} = \left(1,~2\right) $ and $ \vec{v_2} = \left(-2,~-3\right) $ . | 2 |
726 | Find the difference of the vectors $ \vec{v_1} = \left(220,~20\right) $ and $ \vec{v_2} = \left(-180,~318.7\right) $ . | 2 |
727 | Find the magnitude of the vector $ \| \vec{v} \| = \left(2,~12\right) $ . | 2 |
728 | Find the sum of the vectors $ \vec{v_1} = \left(5,~4\right) $ and $ \vec{v_2} = \left(2,~-7\right) $ . | 2 |
729 | Calculate the dot product of the vectors $ \vec{v_1} = \left(9,~6\right) $ and $ \vec{v_2} = \left(-4,~6\right) $ . | 2 |
730 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-4,~-1\right) $ . | 2 |
731 | Find the projection of the vector $ \vec{v_1} = \left(1,~3\right) $ on the vector $ \vec{v_2} = \left(3,~-3\right) $. | 2 |
732 | Find the difference of the vectors $ \vec{v_1} = \left(-\dfrac{ 5387 }{ 125 },~\dfrac{ 68951 }{ 1250 }\right) $ and $ \vec{v_2} = \left(\dfrac{ 10363 }{ 125 },~-\dfrac{ 55919 }{ 1000 }\right) $ . | 2 |
733 | Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~0\right) $ and $ \vec{v_2} = \left(1,~0\right) $ . | 2 |
734 | Find the magnitude of the vector $ \| \vec{v} \| = \left(1,~2\right) $ . | 2 |
735 | Find the projection of the vector $ \vec{v_1} = \left(3,~4\right) $ on the vector $ \vec{v_2} = \left(2,~8\right) $. | 2 |
736 | Find the angle between vectors $ \left(\dfrac{ 3 }{ 5 },~\dfrac{ 4 }{ 5 }\right)$ and $\left(6,~8\right)$. | 2 |
737 | Find the angle between vectors $ \left(-4,~-1\right)$ and $\left(4,~2\right)$. | 2 |
738 | Calculate the dot product of the vectors $ \vec{v_1} = \left(8,~7,~5\right) $ and $ \vec{v_2} = \left(9,~9,~6\right) $ . | 2 |
739 | Find the difference of the vectors $ \vec{v_1} = \left(12,~2\right) $ and $ \vec{v_2} = \left(2,~4\right) $ . | 2 |
740 | Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~3\right) $ and $ \vec{v_2} = \left(2,~1\right) $ . | 2 |
741 | Determine whether the vectors $ \vec{v_1} = \left(4,~4\right) $ and $ \vec{v_2} = \left(5,~5\right) $ are linearly independent or dependent. | 2 |
742 | Find the magnitude of the vector $ \| \vec{v} \| = \left(3,~9\right) $ . | 2 |
743 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-2,~6\right) $ . | 2 |
744 | Find the angle between vectors $ \left(3,~4\right)$ and $\left(1,~2\right)$. | 2 |
745 | Find the magnitude of the vector $ \| \vec{v} \| = \left(0,~8\right) $ . | 2 |
746 | Find the angle between vectors $ \left(8,~7,~5\right)$ and $\left(9,~9,~6\right)$. | 2 |
747 | Find the sum of the vectors $ \vec{v_1} = \left(15,~14\right) $ and $ \vec{v_2} = \left(4,~11\right) $ . | 2 |
748 | Find the difference of the vectors $ \vec{v_1} = \left(0,~-3\right) $ and $ \vec{v_2} = \left(0,~5\right) $ . | 2 |
749 | Find the magnitude of the vector $ \| \vec{v} \| = \left(4,~4\right) $ . | 2 |
750 | Find the difference of the vectors $ \vec{v_1} = \left(1,~2\right) $ and $ \vec{v_2} = \left(1,~2\right) $ . | 2 |