Vectors – Solved Problems Database

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

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ID	Problem	Count
751	Find the sum of the vectors $ \vec{v_1} = \left(-2,~7\right) $ and $ \vec{v_2} = \left(-6,~3\right) $ .	2
752	Find the difference of the vectors $ \vec{v_1} = \left(-3,~5\right) $ and $ \vec{v_2} = \left(1,~-2\right) $ .	2
753	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(0,~0\right) $ .	2
754	Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~-3\right) $ and $ \vec{v_2} = \left(-1,~3\right) $ .	2
755	Find the angle between vectors $ \left(2,~-1\right)$ and $\left(-5,~-4\right)$.	2
756	Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~8\right) $ and $ \vec{v_2} = \left(-8,~-2\right) $ .	2
757	Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~1\right) $ and $ \vec{v_2} = \left(\sqrt{ 3 },~3\right) $ .	2
758	Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~4\right) $ and $ \vec{v_2} = \left(-15,~-20\right) $ .	2
759	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(3,~1\right) $ .	2
760	Determine whether the vectors $ \vec{v_1} = \left(1,~0\right) $ and $ \vec{v_2} = \left(-1,~0\right) $ are linearly independent or dependent.	2
761	Find the sum of the vectors $ \vec{v_1} = \left(1,~1\right) $ and $ \vec{v_2} = \left(-1,~2\right) $ .	2
762	Find the difference of the vectors $ \vec{v_1} = \left(-\dfrac{ 183 }{ 10 },~\dfrac{ 21353 }{ 1000 }\right) $ and $ \vec{v_2} = \left(\dfrac{ 60743 }{ 1000 },~\dfrac{ 1194 }{ 25 }\right) $ .	2
763	Find the sum of the vectors $ \vec{v_1} = \left(8,~8\right) $ and $ \vec{v_2} = \left(-3,~1\right) $ .	2
764	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(8,~7,~0\right) $ .	2
765	Find the sum of the vectors $ \vec{v_1} = \left(8,~7,~0\right) $ and $ \vec{v_2} = \left(6,~-5,~-2\right) $ .	2
766	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(6,~-5,~-2\right) $ .	2
767	Find the angle between vectors $ \left(1,~3\right)$ and $\left(-4,~10\right)$.	2
768	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(-2,~9\right) $ .	2
769	Calculate the dot product of the vectors $ \vec{v_1} = \left(-3,~2\right) $ and $ \vec{v_2} = \left(-4,~-6\right) $ .	2
770	Calculate the dot product of the vectors $ \vec{v_1} = \left(4,~5\right) $ and $ \vec{v_2} = \left(-4,~8\right) $ .	2
771	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(184,~47\right) $ .	2
772	Find the sum of the vectors $ \vec{v_1} = \left(184,~47\right) $ and $ \vec{v_2} = \left(44,~44\right) $ .	2
773	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(1,~8\right) $ .	2
774	Find the projection of the vector $ \vec{v_1} = \left(1,~8\right) $ on the vector $ \vec{v_2} = \left(-3,~-4\right) $.	2
775	Find the angle between vectors $ \left(7,~7\right)$ and $\left(-4,~7\right)$.	2
776	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(-24,~-7\right) $ .	2
777	Find the angle between vectors $ \left(7,~4\right)$ and $\left(-4,~7\right)$.	2
778	Find the sum of the vectors $ \vec{v_1} = \left(6,~9\right) $ and $ \vec{v_2} = \left(4,~1\right) $ .	2
779	Find the difference of the vectors $ \vec{v_1} = \left(6,~9\right) $ and $ \vec{v_2} = \left(4,~1\right) $ .	2
780	Find the sum of the vectors $ \vec{v_1} = \left(5,~-3\right) $ and $ \vec{v_2} = \left(-6,~8\right) $ .	2
781	Find the sum of the vectors $ \vec{v_1} = \left(-20,~0\right) $ and $ \vec{v_2} = \left(16,~-3\right) $ .	2
782	Find the difference of the vectors $ \vec{v_1} = \left(-4,~-3\right) $ and $ \vec{v_2} = \left(-9,~27\right) $ .	2
783	Find the difference of the vectors $ \vec{v_1} = \left(-6,~3\right) $ and $ \vec{v_2} = \left(4,~-9\right) $ .	2
784	Find the angle between vectors $ \left(240,~300\right)$ and $\left(\dfrac{ 29 }{ 10 },~\dfrac{ 307 }{ 100 }\right)$.	2
785	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(3,~9\right) $ .	2
786	Find the projection of the vector $ \vec{v_1} = \left(3,~9\right) $ on the vector $ \vec{v_2} = \left(6,~-3\right) $.	2
787	Find the sum of the vectors $ \vec{v_1} = \left(240,~300\right) $ and $ \vec{v_2} = \left(2.9,~3.08\right) $ .	2
788	Find the sum of the vectors $ \vec{v_1} = \left(855,~130\right) $ and $ \vec{v_2} = \left(775,~135\right) $ .	2
789	Calculate the dot product of the vectors $ \vec{v_1} = \left(-3,~-5\right) $ and $ \vec{v_2} = \left(2,~-8\right) $ .	2
790	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(-12,~-16\right) $ .	2
791	Calculate the dot product of the vectors $ \vec{v_1} = \left(-8,~-5\right) $ and $ \vec{v_2} = \left(-8,~-5\right) $ .	2
792	Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~0\right) $ and $ \vec{v_2} = \left(3,~8\right) $ .	2
793	Calculate the dot product of the vectors $ \vec{v_1} = \left(8,~5\right) $ and $ \vec{v_2} = \left(5,~8\right) $ .	2
794	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(8,~5\right) $ .	2
795	Calculate the dot product of the vectors $ \vec{v_1} = \left(8,~5\right) $ and $ \vec{v_2} = \left(5,~-8\right) $ .	2
796	Find the sum of the vectors $ \vec{v_1} = \left(-10,~5\right) $ and $ \vec{v_2} = \left(-9,~-10\right) $ .	2
797	Find the angle between vectors $ \left(0.866,~\dfrac{ 1 }{ 2 }\right)$ and $\left(-0.7071,~-0.7071\right)$.	2
798	Find the angle between vectors $ \left(-5,~3\right)$ and $\left(2,~6\right)$.	2
799	Find the difference of the vectors $ \vec{v_1} = \left(-\dfrac{ 3 }{ 8 },~\dfrac{ 7 }{ 8 }\right) $ and $ \vec{v_2} = \left(8,~22\right) $ .	2
800	Find the projection of the vector $ \vec{v_1} = \left(-2,~0,~-3\right) $ on the vector $ \vec{v_2} = \left(1,~-3,~-1\right) $.	2