Vectors

(the database of solved problems)

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

Select category

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