Vectors – Solved Problems Database

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

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ID	Problem	Count
651	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(-4,~0\right) $ .	2
652	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(0,~0\right) $ .	2
653	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(2,~-2,~2\right) $ .	2
654	Find the projection of the vector $ \vec{v_1} = \left(-2,~3,~1\right) $ on the vector $ \vec{v_2} = \left(1,~1,~2\right) $.	2
655	Find the angle between vectors $ \left(3,~4\right)$ and $\left(6,~8\right)$.	2
656	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
657	Find the angle between vectors $ \left(-2,~3,~1\right)$ and $\left(1,~1,~2\right)$.	2
658	Find the projection of the vector $ \vec{v_1} = \left(3,~-4\right) $ on the vector $ \vec{v_2} = \left(-18,~24\right) $.	2
659	Find the sum of the vectors $ \vec{v_1} = \left(4,~-3\right) $ and $ \vec{v_2} = \left(1,~5\right) $ .	2
660	Find the difference of the vectors $ \vec{v_1} = \left(-2,~5\right) $ and $ \vec{v_2} = \left(4,~1\right) $ .	2
661	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
662	Find the angle between vectors $ \left(8,~7,~5\right)$ and $\left(9,~9,~6\right)$.	2
663	Find the sum of the vectors $ \vec{v_1} = \left(3,~4\right) $ and $ \vec{v_2} = \left(5,~-1\right) $ .	2
664	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(4,~2\right) $ .	2
665	Find the sum of the vectors $ \vec{v_1} = \left(0,~3\right) $ and $ \vec{v_2} = \left(3,~7\right) $ .	2
666	Find the sum of the vectors $ \vec{v_1} = \left(0,~-5\right) $ and $ \vec{v_2} = \left(-5,~5\right) $ .	2
667	Find the sum of the vectors $ \vec{v_1} = \left(0,~6\right) $ and $ \vec{v_2} = \left(2,~1\right) $ .	2
668	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(-2,~3,~1\right) $ .	2
669	Calculate the cross product of the vectors $ \vec{v_1} = \left(-3,~8,~0\right) $ and $ \vec{v_2} = \left(-7,~6,~0\right) $ .	2
670	Calculate the cross product of the vectors $ \vec{v_1} = \left(-3,~8,~0\right) $ and $ \vec{v_2} = \left(-2,~6,~0\right) $ .	2
671	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(1,~1\right) $ .	2
672	Find the angle between vectors $ \left(1,~0\right)$ and $\left(-1,~0\right)$.	2
673	Find the sum of the vectors $ \vec{v_1} = \left(1,~0\right) $ and $ \vec{v_2} = \left(-\dfrac{ 1 }{ 2 },~\dfrac{\sqrt{ 3 }}{ 2 }\right) $ .	2
674	Find the projection of the vector $ \vec{v_1} = \left(2,~-1\right) $ on the vector $ \vec{v_2} = \left(-1,~3\right) $.	2
675	Find the angle between vectors $ \left(2,~-1\right)$ and $\left(-1,~3\right)$.	2
676	Find the projection of the vector $ \vec{v_1} = \left(1,~1,~1\right) $ on the vector $ \vec{v_2} = \left(0,~2,~1\right) $.	2
677	Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~1,~2\right) $ and $ \vec{v_2} = \left(1,~1,~5\right) $ .	2
678	Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~1,~1\right) $ and $ \vec{v_2} = \left(2,~1,~0\right) $ .	2
679	Find the difference of the vectors $ \vec{v_1} = \left(10,~-4\right) $ and $ \vec{v_2} = \left(0,~-1\right) $ .	2
680	Find the difference of the vectors $ \vec{v_1} = \left(2,~-3\right) $ and $ \vec{v_2} = \left(3,~4\right) $ .	2
681	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
682	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(\dfrac{ 7 }{ 5 },~\dfrac{ 7 }{ 5 }\right) $ .	2
683	Calculate the dot product of the vectors $ \vec{v_1} = \left(\dfrac{ 7 }{ 5 },~\dfrac{ 7 }{ 5 }\right) $ and $ \vec{v_2} = \left(4,~-4\right) $ .	2
684	Find the sum of the vectors $ \vec{v_1} = \left(8,~0\right) $ and $ \vec{v_2} = \left(\dfrac{ 529919 }{ 100000 },~\dfrac{ 53003 }{ 6250 }\right) $ .	2
685	Find the difference of the vectors $ \vec{v_1} = \left(-2,~5\right) $ and $ \vec{v_2} = \left(6,~3\right) $ .	2
686	Find the angle between vectors $ \left(0,~-1\right)$ and $\left(4,~1\right)$.	2
687	Find the angle between vectors $ \left(1,~-2\right)$ and $\left(4,~1\right)$.	2
688	Find the sum of the vectors $ \vec{v_1} = \left(2,~-3\right) $ and $ \vec{v_2} = \left(-2,~3\right) $ .	2
689	Find the sum of the vectors $ \vec{v_1} = \left(2,~-3\right) $ and $ \vec{v_2} = \left(-3,~2\right) $ .	2
690	Find the sum of the vectors $ \vec{v_1} = \left(2,~-3\right) $ and $ \vec{v_2} = \left(-3,~-2\right) $ .	2
691	Find the sum of the vectors $ \vec{v_1} = \left(-2,~-3\right) $ and $ \vec{v_2} = \left(2,~-3\right) $ .	2
692	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(-4,~-2\right) $ .	2
693	Find the sum of the vectors $ \vec{v_1} = \left(5,~8\right) $ and $ \vec{v_2} = \left(-9,~2\right) $ .	2
694	Find the sum of the vectors $ \vec{v_1} = \left(6,~-5\right) $ and $ \vec{v_2} = \left(-4,~5\right) $ .	2
695	Calculate the cross product of the vectors $ \vec{v_1} = \left(5,~-2,~2\right) $ and $ \vec{v_2} = \left(-20,~8,~-8\right) $ .	2
696	Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~-4\right) $ and $ \vec{v_2} = \left(-1,~2\right) $ .	2
697	Calculate the dot product of the vectors $ \vec{v_1} = \left(-3,~5\right) $ and $ \vec{v_2} = \left(-24,~40\right) $ .	2
698	Find the sum of the vectors $ \vec{v_1} = \left(9,~-4\right) $ and $ \vec{v_2} = \left(-10,~7\right) $ .	2
699	Find the difference of the vectors $ \vec{v_1} = \left(8,~-6\right) $ and $ \vec{v_2} = \left(-4,~8\right) $ .	2
700	Find the sum of the vectors $ \vec{v_1} = \left(-36,~20\right) $ and $ \vec{v_2} = \left(-2,~-4\right) $ .	2