Vectors – Solved Problems Database

All the problems and solutions shown below were generated using the Vectors Calculator.

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ID	Problem	Count
601	Find the difference of the vectors $ \vec{v_1} = \left(5,~3\right) $ and $ \vec{v_2} = \left(3,~5\right) $ .	2
602	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(-2,~4\right) $ .	2
603	Calculate the dot product of the vectors $ \vec{v_1} = \left(0,~9\right) $ and $ \vec{v_2} = \left(-5,~2\right) $ .	2
604	Calculate the dot product of the vectors $ \vec{v_1} = \left(0,~9\right) $ and $ \vec{v_2} = \left(-5,~2\right) $ .	2
605	Find the difference of the vectors $ \vec{v_1} = \left(-1,~2\right) $ and $ \vec{v_2} = \left(4,~26\right) $ .	2
606	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(-\dfrac{ 8 }{ 17 },~\dfrac{ 15 }{ 17 }\right) $ .	2
607	Find the sum of the vectors $ \vec{v_1} = \left(\dfrac{ 20 }{ 7 },~-\dfrac{ 25 }{ 7 }\right) $ and $ \vec{v_2} = \left(15,~78\right) $ .	2
608	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(\dfrac{ 72 }{ 41 },~-\dfrac{ 320 }{ 41 }\right) $ .	2
609	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(\dfrac{ 2 }{ 3 },~\sqrt{ 3 },~2\right) $ .	2
610	Calculate the dot product of the vectors $ \vec{v_1} = \left(\dfrac{ 1 }{ 2 },~\sqrt{ 3 },~5\right) $ and $ \vec{v_2} = \left(4,~-\sqrt{ 3 },~10\right) $ .	2
611	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(9,~40\right) $ .	2
612	Find the angle between vectors $ \left(4,~-1\right)$ and $\left(3,~2\right)$.	2
613	Find the sum of the vectors $ \vec{v_1} = \left(-\dfrac{ 2 }{ 5 },~\dfrac{ 4 }{ 5 }\right) $ and $ \vec{v_2} = \left(9,~26\right) $ .	2
614	Find the difference of the vectors $ \vec{v_1} = \left(-\dfrac{ 1 }{ 5 },~\dfrac{ 3 }{ 5 }\right) $ and $ \vec{v_2} = \left(3,~28\right) $ .	2
615	Find the sum of the vectors $ \vec{v_1} = \left(-\dfrac{ 4 }{ 9 },~-\dfrac{ 16 }{ 9 }\right) $ and $ \vec{v_2} = \left(36,~100\right) $ .	2
616	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(-\dfrac{ 100493 }{ 1000 },~-\dfrac{ 1419 }{ 500 }\right) $ .	2
617	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(\dfrac{ 14 }{ 5 },~\dfrac{ 123 }{ 5 }\right) $ .	2
618	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(-\dfrac{ 3 }{ 5 },~\dfrac{ 4 }{ 5 }\right) $ .	2
619	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(9,~40\right) $ .	2
620	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(5,~12\right) $ .	2
621	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(-1,~0,~2\right) $ .	2
622	Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~-7\right) $ and $ \vec{v_2} = \left(5,~9\right) $ .	2
623	Find the projection of the vector $ \vec{v_1} = \left(2,~-7\right) $ on the vector $ \vec{v_2} = \left(5,~9\right) $.	2
624	Find the sum of the vectors $ \vec{v_1} = \left(2,~-7\right) $ and $ \vec{v_2} = \left(5,~9\right) $ .	2
625	Find the angle between vectors $ \left(3,~2\right)$ and $\left(1,~-4\right)$.	2
626	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(-5,~6\right) $ .	2
627	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(-9,~7\right) $ .	2
628	Find the angle between vectors $ \left(2,~-1\right)$ and $\left(2,~3\right)$.	2
629	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(-2,~6\right) $ .	2
630	Calculate the dot product of the vectors $ \vec{v_1} = \left(9,~3\right) $ and $ \vec{v_2} = \left(-8,~5\right) $ .	2
631	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(-\dfrac{ 8 }{ 17 },~\dfrac{ 15 }{ 17 }\right) $ .	2
632	Find the sum of the vectors $ \vec{v_1} = \left(-\dfrac{ 15 }{ 7 },~\dfrac{ 30 }{ 7 }\right) $ and $ \vec{v_2} = \left(10,~46\right) $ .	2
633	Find the angle between vectors $ \left(0,~5\right)$ and $\left(6,~6\right)$.	2
634	Calculate the dot product of the vectors $ \vec{v_1} = \left(5,~5\right) $ and $ \vec{v_2} = \left(-7,~4\right) $ .	2
635	Find the angle between vectors $ \left(-6,~4\right)$ and $\left(3,~3\right)$.	2
636	Find the angle between vectors $ \left(0,~-5,~5\right)$ and $\left(3,~1,~1\right)$.	2
637	Find the angle between vectors $ \left(5,~3\right)$ and $\left(1,~3\right)$.	2
638	Calculate the dot product of the vectors $ \vec{v_1} = \left(5,~3\right) $ and $ \vec{v_2} = \left(-7,~-14\right) $ .	2
639	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(4,~6\right) $ .	2
640	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(1,~0\right) $ .	2
641	Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~3\right) $ and $ \vec{v_2} = \left(-1,~2\right) $ .	2
642	Find the difference of the vectors $ \vec{v_1} = \left(9,~-7\right) $ and $ \vec{v_2} = \left(-10,~7\right) $ .	2
643	Find the difference of the vectors $ \vec{v_1} = \left(1,~0,~0\right) $ and $ \vec{v_2} = \left(0,~1,~0\right) $ .	2
644	Find the sum of the vectors $ \vec{v_1} = \left(1,~0,~0\right) $ and $ \vec{v_2} = \left(0,~1,~0\right) $ .	2
645	Find the difference of the vectors $ \vec{v_1} = \left(3,~1\right) $ and $ \vec{v_2} = \left(-2,~-2\right) $ .	2
646	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(50,~105\right) $ .	2
647	Find the angle between vectors $ \left(-4,~-3\right)$ and $\left(-1,~3\right)$.	2
648	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(-3,~1\right) $ .	2
649	Find the angle between vectors $ \left(-4,~3\right)$ and $\left(5,~7\right)$.	2
650	Calculate the dot product of the vectors $ \vec{v_1} = \left(4,~1\right) $ and $ \vec{v_2} = \left(2,~-6\right) $ .	2