Vectors – Solved Problems Database
All the problems and solutions shown below were generated using the Vectors Calculator.
ID |
Problem |
Count |
651 | Find the sum of the vectors $ \vec{v_1} = \left(1,~-2\right) $ and $ \vec{v_2} = \left(-5,~0\right) $ . | 2 |
652 | Find the difference of the vectors $ \vec{v_1} = \left(1,~\sqrt{ 3 }\right) $ and $ \vec{v_2} = \left(-\dfrac{ 1 }{ 2 },~\dfrac{\sqrt{ 3 }}{ 2 }\right) $ . | 2 |
653 | Find the magnitude of the vector $ \| \vec{v} \| = \left(6,~-15\right) $ . | 2 |
654 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-3,~0\right) $ and $ \vec{v_2} = \left(1,~0\right) $ . | 2 |
655 | Find the angle between vectors $ \left(2,~-1\right)$ and $\left(6,~4\right)$. | 2 |
656 | Find the angle between vectors $ \left(4,~-4\right)$ and $\left(-1,~-3\right)$. | 2 |
657 | Find the sum of the vectors $ \vec{v_1} = \left(-36,~20\right) $ and $ \vec{v_2} = \left(-2,~-4\right) $ . | 2 |
658 | Find the difference of the vectors $ \vec{v_1} = \left(220,~40\right) $ and $ \vec{v_2} = \left(-150,~309.23\right) $ . | 2 |
659 | Calculate the dot product of the vectors $ \vec{v_1} = \left(\dfrac{ 3 }{ 2 },~\dfrac{\sqrt{ 3 }}{ 2 }\right) $ and $ \vec{v_2} = \left(-1,~\sqrt{ 3 }\right) $ . | 2 |
660 | Find the angle between vectors $ \left(-3,~0\right)$ and $\left(1,~0\right)$. | 2 |
661 | Find the angle between vectors $ \left(4,~-1\right)$ and $\left(-3,~5\right)$. | 2 |
662 | Find the projection of the vector $ \vec{v_1} = \left(-3,~5,~2\right) $ on the vector $ \vec{v_2} = \left(0,~1,~0\right) $. | 2 |
663 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-5,~6\right) $ . | 2 |
664 | Find the projection of the vector $ \vec{v_1} = \left(2,~5\right) $ on the vector $ \vec{v_2} = \left(-2,~1\right) $. | 2 |
665 | Calculate the dot product of the vectors $ \vec{v_1} = \left(5,~0\right) $ and $ \vec{v_2} = \left(5,~0\right) $ . | 2 |
666 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-4,~-1\right) $ . | 2 |
667 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-3,~-1\right) $ . | 2 |
668 | Find the angle between vectors $ \left(6,~-5,~-3\right)$ and $\left(4,~2,~2\right)$. | 2 |
669 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-6,~-4\right) $ . | 2 |
670 | Find the sum of the vectors $ \vec{v_1} = \left(2,~4\right) $ and $ \vec{v_2} = \left(3,~-2\right) $ . | 2 |
671 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-2,~4\right) $ . | 2 |
672 | Find the projection of the vector $ \vec{v_1} = \left(-9,~-4\right) $ on the vector $ \vec{v_2} = \left(-11,~-8\right) $. | 2 |
673 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-3,~2\right) $ and $ \vec{v_2} = \left(-4,~-6\right) $ . | 2 |
674 | Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~-3\right) $ and $ \vec{v_2} = \left(4,~3\right) $ . | 2 |
675 | Calculate the dot product of the vectors $ \vec{v_1} = \left(5,~0,~5\right) $ and $ \vec{v_2} = \left(5,~5 \sqrt{ 2 },~5\right) $ . | 2 |
676 | Find the angle between vectors $ \left(3,~4\right)$ and $\left(-3,~7\right)$. | 2 |
677 | Find the angle between vectors $ \left(\dfrac{ 3 }{ 5 },~\dfrac{ 1 }{ 5 }\right)$ and $\left(\dfrac{ 2 }{ 5 },~\dfrac{ 4 }{ 5 }\right)$. | 2 |
678 | Find the difference of the vectors $ \vec{v_1} = \left(2,~6\right) $ and $ \vec{v_2} = \left(0,~-5\right) $ . | 2 |
679 | Find the angle between vectors $ \left(5,~-1\right)$ and $\left(3,~2\right)$. | 2 |
680 | Find the difference of the vectors $ \vec{v_1} = \left(4,~3\right) $ and $ \vec{v_2} = \left(3,~5\right) $ . | 2 |
681 | Find the projection of the vector $ \vec{v_1} = \left(-3,~0\right) $ on the vector $ \vec{v_2} = \left(5,~0\right) $. | 2 |
682 | Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~2,~3\right) $ and $ \vec{v_2} = \left(1,~1,~2\right) $ . | 2 |
683 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-30,~23\right) $ . | 2 |
684 | Find the magnitude of the vector $ \| \vec{v} \| = \left(-9,~7\right) $ . | 2 |
685 | Find the difference of the vectors $ \vec{v_1} = \left(10,~8\right) $ and $ \vec{v_2} = \left(-4,~10\right) $ . | 2 |
686 | Calculate the cross product of the vectors $ \vec{v_1} = \left(-8,~-3,~3\right) $ and $ \vec{v_2} = \left(-2,~-2,~-8\right) $ . | 2 |
687 | Find the magnitude of the vector $ \| \vec{v} \| = \left(3,~-2\right) $ . | 2 |
688 | Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~3,~-2\right) $ and $ \vec{v_2} = \left(1,~-2,~3\right) $ . | 2 |
689 | Find the angle between vectors $ \left(3,~4\right)$ and $\left(3,~-4\right)$. | 2 |
690 | Find the difference of the vectors $ \vec{v_1} = \left(230,~6.67\right) $ and $ \vec{v_2} = \left(-150,~309.23\right) $ . | 2 |
691 | Find the sum of the vectors $ \vec{v_1} = \left(1,~4\right) $ and $ \vec{v_2} = \left(-2,~5\right) $ . | 2 |
692 | Find the magnitude of the vector $ \| \vec{v} \| = \left(5,~0,~5\right) $ . | 2 |
693 | Find the magnitude of the vector $ \| \vec{v} \| = \left(\dfrac{ 1 }{ 4 },~\dfrac{ 1 }{ 8 }\right) $ . | 2 |
694 | Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~3,~-2\right) $ and $ \vec{v_2} = \left(-8,~5,~6\right) $ . | 2 |
695 | Find the projection of the vector $ \vec{v_1} = \left(4,~3\right) $ on the vector $ \vec{v_2} = \left(0,~1\right) $. | 2 |
696 | Find the magnitude of the vector $ \| \vec{v} \| = \left(0,~5\right) $ . | 2 |
697 | Find the angle between vectors $ \left(240,~300\right)$ and $\left(\dfrac{ 29 }{ 10 },~\dfrac{ 307 }{ 100 }\right)$. | 2 |
698 | Find the magnitude of the vector $ \| \vec{v} \| = \left(5,~6\right) $ . | 2 |
699 | Calculate the dot product of the vectors $ \vec{v_1} = \left(-8,~\sqrt{ 7 }\right) $ and $ \vec{v_2} = \left(64,~36\right) $ . | 2 |
700 | Find the sum of the vectors $ \vec{v_1} = \left(5,~7\right) $ and $ \vec{v_2} = \left(-1,~1\right) $ . | 2 |