Vectors – Solved Problems Database

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

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ID	Problem	Count
801	Find the angle between vectors $ \left(-2,~0,~-3\right)$ and $\left(1,~-3,~-1\right)$.	2
802	Find the projection of the vector $ \vec{v_1} = \left(-5,~2,~0\right) $ on the vector $ \vec{v_2} = \left(-1,~8,~-4\right) $.	2
803	Calculate the dot product of the vectors $ \vec{v_1} = \left(9,~9,~9\right) $ and $ \vec{v_2} = \left(9,~9,~9\right) $ .	2
804	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(4,~5\right) $ .	2
805	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(-2,~-4\right) $ .	2
806	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(-\dfrac{ 3 }{ 5 },~\dfrac{ 4 }{ 5 }\right) $ .	2
807	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(-\dfrac{ 9 }{ 41 },~\dfrac{ 40 }{ 41 }\right) $ .	2
808	Find the angle between vectors $ \left(-1,~6\right)$ and $\left(2,~7\right)$.	2
809	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(-0.3846,~0.9231\right) $ .	2
810	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(0.8,~0.2\right) $ .	2
811	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(-\dfrac{ 3 }{ 5 },~\dfrac{ 4 }{ 5 }\right) $ .	2
812	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(-3,~2\right) $ .	2
813	Find the difference of the vectors $ \vec{v_1} = \left(-3,~4\right) $ and $ \vec{v_2} = \left(-2,~7\right) $ .	2
814	Calculate the dot product of the vectors $ \vec{v_1} = \left(0,~\dfrac{ 1 }{ 2 }\right) $ and $ \vec{v_2} = \left(0,~0\right) $ .	2
815	Find the sum of the vectors $ \vec{v_1} = \left(\dfrac{ 8 }{ 9 },~-\dfrac{ 40 }{ 9 }\right) $ and $ \vec{v_2} = \left(6,~56\right) $ .	2
816	Find the projection of the vector $ \vec{v_1} = \left(2,~-5\right) $ on the vector $ \vec{v_2} = \left(-6,~-4\right) $.	2
817	Find the angle between vectors $ \left(3,~5\right)$ and $\left(0,~-4\right)$.	2
818	Find the projection of the vector $ \vec{v_1} = \left(3,~5\right) $ on the vector $ \vec{v_2} = \left(0,~-4\right) $.	2
819	Find the angle between vectors $ \left(\dfrac{ 8 }{ 3 },~\dfrac{ 8 }{ 3 }\right)$ and $\left(7,~-7\right)$.	2
820	Calculate the dot product of the vectors $ \vec{v_1} = \left(\dfrac{ 8 }{ 3 },~\dfrac{ 8 }{ 3 }\right) $ and $ \vec{v_2} = \left(7,~-7\right) $ .	2
821	Find the angle between vectors $ \left(-\dfrac{ 1 }{ 2 },~- \dfrac{\sqrt{ 3 }}{ 2 }\right)$ and $\left(\dfrac{\sqrt{ 2 }}{ 2 },~- \dfrac{\sqrt{ 2 }}{ 2 }\right)$.	2
822	Find the projection of the vector $ \vec{v_1} = \left(-\dfrac{ 1 }{ 2 },~- \dfrac{\sqrt{ 3 }}{ 2 }\right) $ on the vector $ \vec{v_2} = \left(\dfrac{\sqrt{ 2 }}{ 2 },~- \dfrac{\sqrt{ 2 }}{ 2 }\right) $.	2
823	Find the angle between vectors $ \left(5,~-2\right)$ and $\left(-7,~-3\right)$.	2
824	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(-1,~-3\right) $ .	2
825	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(-5,~2\right) $ .	2
826	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(5,~-2\right) $ .	2
827	Find the difference of the vectors $ \vec{v_1} = \left(3,~9\right) $ and $ \vec{v_2} = \left(-6,~-7\right) $ .	2
828	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(1,~2\right) $ .	2
829	Find the difference of the vectors $ \vec{v_1} = \left(1,~2\right) $ and $ \vec{v_2} = \left(1,~2\right) $ .	2
830	Find the projection of the vector $ \vec{v_1} = \left(\dfrac{ 4 }{ 3 },~-6\right) $ on the vector $ \vec{v_2} = \left(9,~-\dfrac{ 3 }{ 2 }\right) $.	2
831	Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~2,~-3\right) $ and $ \vec{v_2} = \left(4,~-5,~6\right) $ .	2
832	Calculate the dot product of the vectors $ \vec{v_1} = \left(7,~1\right) $ and $ \vec{v_2} = \left(2,~9\right) $ .	2
833	Find the angle between vectors $ \left(7,~1\right)$ and $\left(2,~9\right)$.	2
834	Find the sum of the vectors $ \vec{v_1} = \left(2,~1\right) $ and $ \vec{v_2} = \left(1,~3\right) $ .	2
835	Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~2,~-4\right) $ and $ \vec{v_2} = \left(4,~-5,~6\right) $ .	2
836	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(1,~13\right) $ .	2
837	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(2,~10\right) $ .	2
838	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(-5,~-5\right) $ .	2
839	Find the difference of the vectors $ \vec{v_1} = \left(-3,~10\right) $ and $ \vec{v_2} = \left(5,~7\right) $ .	2
840	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(0,~0\right) $ .	2
841	Calculate the dot product of the vectors $ \vec{v_1} = \left(-3,~10\right) $ and $ \vec{v_2} = \left(5,~7\right) $ .	2
842	Find the angle between vectors $ \left(-3,~10\right)$ and $\left(5,~7\right)$.	2
843	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(15,~-41\right) $ .	2
844	Find the sum of the vectors $ \vec{v_1} = \left(15,~-41\right) $ and $ \vec{v_2} = \left(29,~37\right) $ .	2
845	Find the projection of the vector $ \vec{v_1} = \left(2345,~2234\right) $ on the vector $ \vec{v_2} = \left(4721,~4576\right) $.	2
846	Find the sum of the vectors $ \vec{v_1} = \left(9,~8\right) $ and $ \vec{v_2} = \left(2,~0\right) $ .	2
847	Calculate the dot product of the vectors $ \vec{v_1} = \left(8,~-7\right) $ and $ \vec{v_2} = \left(-11,~-4\right) $ .	2
848	Find the angle between vectors $ \left(4,~-5\right)$ and $\left(3,~7\right)$.	2
849	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(80,~28\right) $ .	2
850	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(2,~10\right) $ .	2