Vectors

(the database of solved problems)

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

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ID	Problem	Count
901	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(-15,~-8\right) $ .	2
902	Find the angle between vectors $ \left(-15,~-8\right)$ and $\left(-1,~9\right)$.	2
903	Find the angle between vectors $ \left(3,~-2\right)$ and $\left(-1,~5\right)$.	2
904	Find the projection of the vector $ \vec{v_1} = \left(4,~0\right) $ on the vector $ \vec{v_2} = \left(5,~-2\right) $.	2
905	Find the projection of the vector $ \vec{v_1} = \left(4,~-4\right) $ on the vector $ \vec{v_2} = \left(5,~-4\right) $.	2
906	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(\dfrac{ 7 }{ 10 },~\dfrac{ 3 }{ 10 }\right) $ .	2
907	Find the angle between vectors $ \left(7,~5\right)$ and $\left(9,~0\right)$.	2
908	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(6,~-6\right) $ .	2
909	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(4,~-6\right) $ .	2
910	Calculate the dot product of the vectors $ \vec{v_1} = \left(8,~-4\right) $ and $ \vec{v_2} = \left(5,~1\right) $ .	2
911	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(4,~-3\right) $ .	2
912	Find the projection of the vector $ \vec{v_1} = \left(-1,~3\right) $ on the vector $ \vec{v_2} = \left(4,~4\right) $.	2
913	Find the sum of the vectors $ \vec{v_1} = \left(-1,~0\right) $ and $ \vec{v_2} = \left(-4,~-5\right) $ .	2
914	Find the difference of the vectors $ \vec{v_1} = \left(-1,~0\right) $ and $ \vec{v_2} = \left(-4,~-5\right) $ .	2
915	Find the sum of the vectors $ \vec{v_1} = \left(2,~3\right) $ and $ \vec{v_2} = \left(-1,~1\right) $ .	2
916	Find the difference of the vectors $ \vec{v_1} = \left(3,~-3\right) $ and $ \vec{v_2} = \left(24,~6\right) $ .	2
917	Find the angle between vectors $ \left(3,~4\right)$ and $\left(1,~2\right)$.	2
918	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(3,~4\right) $ .	2
919	Determine whether the vectors $ \vec{v_1} = \left(\dfrac{ 3 }{ 2 },~2\right) $ and $ \vec{v_2} = \left(\dfrac{ 7 }{ 2 },~-7\right) $ are linearly independent or dependent.	2
920	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(-4,~-8\right) $ .	2
921	Calculate the dot product of the vectors $ \vec{v_1} = \left(-\dfrac{ 4 }{ 3 },~\dfrac{ 5 }{ 2 }\right) $ and $ \vec{v_2} = \left(16,~-30\right) $ .	2
922	Find the angle between vectors $ \left(-\dfrac{ 4 }{ 3 },~\dfrac{ 5 }{ 2 }\right)$ and $\left(16,~-30\right)$.	2
923	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(8,~-6\right) $ .	2
924	Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~2\right) $ and $ \vec{v_2} = \left(-9,~-2\right) $ .	2
925	Calculate the dot product of the vectors $ \vec{v_1} = \left(-1,~5\right) $ and $ \vec{v_2} = \left(6,~8\right) $ .	2
926	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(2,~0\right) $ .	2
927	Find the angle between vectors $ \left(-5,~9\right)$ and $\left(7,~-1\right)$.	2
928	Find the angle between vectors $ \left(2,~5\right)$ and $\left(-3,~4\right)$.	2
929	Find the angle between vectors $ \left(8,~4\right)$ and $\left(-2,~4\right)$.	2
930	Find the angle between vectors $ \left(6,~-8\right)$ and $\left(-1,~8\right)$.	2
931	Find the angle between vectors $ \left(-2,~-3\right)$ and $\left(-2,~2\right)$.	2
932	Calculate the dot product of the vectors $ \vec{v_1} = \left(0,~-12\right) $ and $ \vec{v_2} = \left(\dfrac{ 1 }{ 2 },~0\right) $ .	2
933	Find the sum of the vectors $ \vec{v_1} = \left(7,~9\right) $ and $ \vec{v_2} = \left(4,~6\right) $ .	2
934	Find the projection of the vector $ \vec{v_1} = \left(7,~7\right) $ on the vector $ \vec{v_2} = \left(-8,~5\right) $.	2
935	Calculate the cross product of the vectors $ \vec{v_1} = \left(2,~-1,~1\right) $ and $ \vec{v_2} = \left(10,~-12,~5\right) $ .	2
936	Calculate the cross product of the vectors $ \vec{v_1} = \left(2,~-1,~1\right) $ and $ \vec{v_2} = \left(6,~-4,~3\right) $ .	2
937	Calculate the cross product of the vectors $ \vec{v_1} = \left(2,~-1,~1\right) $ and $ \vec{v_2} = \left(6,~-8,~3\right) $ .	2
938	Find the angle between vectors $ \left(-4,~2,~-5\right)$ and $\left(1,~1,~3\right)$.	2
939	Find the sum of the vectors $ \vec{v_1} = \left(6,~0\right) $ and $ \vec{v_2} = \left(8,~0\right) $ .	2
940	Find the difference of the vectors $ \vec{v_1} = \left(6,~0\right) $ and $ \vec{v_2} = \left(8,~0\right) $ .	2
941	Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~2\right) $ and $ \vec{v_2} = \left(1,~0\right) $ .	2
942	Calculate the dot product of the vectors $ \vec{v_1} = \left(7,~8\right) $ and $ \vec{v_2} = \left(5,~4\right) $ .	2
943	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(1,~0\right) $ .	2
944	Find the sum of the vectors $ \vec{v_1} = \left(3,~4\right) $ and $ \vec{v_2} = \left(-2,~5\right) $ .	2
945	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(7,~7\right) $ .	2
946	Calculate the dot product of the vectors $ \vec{v_1} = \left(7,~7\right) $ and $ \vec{v_2} = \left(-8,~1\right) $ .	2
947	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(2,~2\right) $ .	2
948	Calculate the dot product of the vectors $ \vec{v_1} = \left(4,~5\right) $ and $ \vec{v_2} = \left(1,~6\right) $ .	2
949	Find the sum of the vectors $ \vec{v_1} = \left(-3,~8\right) $ and $ \vec{v_2} = \left(5,~-5\right) $ .	2
950	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