Vectors – Solved Problems Database

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

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ID	Problem	Count
701	Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~4\right) $ and $ \vec{v_2} = \left(1,~4\right) $ .	2
702	Calculate the dot product of the vectors $ \vec{v_1} = \left(7,~-3\right) $ and $ \vec{v_2} = \left(7,~-3\right) $ .	2
703	Calculate the dot product of the vectors $ \vec{v_1} = \left(-7,~-3\right) $ and $ \vec{v_2} = \left(-10,~-5\right) $ .	2
704	Calculate the dot product of the vectors $ \vec{v_1} = \left(-7,~-3\right) $ and $ \vec{v_2} = \left(-7,~-3\right) $ .	2
705	Find the angle between vectors $ \left(5,~-1\right)$ and $\left(2,~3\right)$.	2
706	Find the angle between vectors $ \left(4,~-5\right)$ and $\left(8,~-1\right)$.	2
707	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(9,~12\right) $ .	2
708	Calculate the dot product of the vectors $ \vec{v_1} = \left(10,~8\right) $ and $ \vec{v_2} = \left(-10,~-9\right) $ .	2
709	Find the sum of the vectors $ \vec{v_1} = \left(-1,~5\right) $ and $ \vec{v_2} = \left(7,~-8\right) $ .	2
710	Find the difference of the vectors $ \vec{v_1} = \left(-6,~8\right) $ and $ \vec{v_2} = \left(4,~-7\right) $ .	2
711	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(8,~7\right) $ .	2
712	Find the difference of the vectors $ \vec{v_1} = \left(7,~5\right) $ and $ \vec{v_2} = \left(-2,~-3\right) $ .	2
713	Calculate the dot product of the vectors $ \vec{v_1} = \left(-1,~4\right) $ and $ \vec{v_2} = \left(3,~-2\right) $ .	2
714	Find the difference of the vectors $ \vec{v_1} = \left(5,~-4\right) $ and $ \vec{v_2} = \left(-2,~3\right) $ .	2
715	Find the sum of the vectors $ \vec{v_1} = \left(7,~-3\right) $ and $ \vec{v_2} = \left(-3,~-5\right) $ .	2
716	Find the sum of the vectors $ \vec{v_1} = \left(-6,~-5\right) $ and $ \vec{v_2} = \left(7,~10\right) $ .	2
717	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(5,~4\right) $ .	2
718	Calculate the dot product of the vectors $ \vec{v_1} = \left(5,~4\right) $ and $ \vec{v_2} = \left(-8,~5\right) $ .	2
719	Calculate the dot product of the vectors $ \vec{v_1} = \left(1,~5\right) $ and $ \vec{v_2} = \left(-3,~9\right) $ .	2
720	Find the sum of the vectors $ \vec{v_1} = \left(7,~-5\right) $ and $ \vec{v_2} = \left(-3,~-4\right) $ .	2
721	Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~1\right) $ and $ \vec{v_2} = \left(1,~4\right) $ .	2
722	Find the difference of the vectors $ \vec{v_1} = \left(-2,~4\right) $ and $ \vec{v_2} = \left(6,~-4\right) $ .	2
723	Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~3\right) $ and $ \vec{v_2} = \left(-4,~2\right) $ .	2
724	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(6,~4\right) $ .	2
725	Find the angle between vectors $ \left(-3,~8\right)$ and $\left(4,~12\right)$.	2
726	Calculate the dot product of the vectors $ \vec{v_1} = \left(-1,~2\right) $ and $ \vec{v_2} = \left(7,~17\right) $ .	2
727	Find the projection of the vector $ \vec{v_1} = \left(-7,~7\right) $ on the vector $ \vec{v_2} = \left(1,~22\right) $.	2
728	Find the difference of the vectors $ \vec{v_1} = \left(-7,~7\right) $ and $ \vec{v_2} = \left(1,~22\right) $ .	2
729	Find the difference of the vectors $ \vec{v_1} = \left(-1,~2\right) $ and $ \vec{v_2} = \left(7,~17\right) $ .	2
730	Calculate the dot product of the vectors $ \vec{v_1} = \left(-7,~7\right) $ and $ \vec{v_2} = \left(1,~22\right) $ .	2
731	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(1,~-3,~2\right) $ .	2
732	Find the difference of the vectors $ \vec{v_1} = \left(3,~-4\right) $ and $ \vec{v_2} = \left(-3,~8\right) $ .	2
733	Find the magnitude of the vector $ \\| \vec{v} \\| = \left(\dfrac{ 1 }{ 4 },~\dfrac{ 3 }{ 4 }\right) $ .	2
734	Find the difference of the vectors $ \vec{v_1} = \left(3,~-4\right) $ and $ \vec{v_2} = \left(-4,~8\right) $ .	2
735	Find the angle between vectors $ \left(2,~-1\right)$ and $\left(8,~3\right)$.	2
736	Calculate the dot product of the vectors $ \vec{v_1} = \left(3,~4\right) $ and $ \vec{v_2} = \left(8,~2\right) $ .	2
737	Calculate the dot product of the vectors $ \vec{v_1} = \left(\dfrac{ 8 }{ 17 },~\dfrac{ 8 }{ 17 }\right) $ and $ \vec{v_2} = \left(8,~2\right) $ .	2
738	Find the sum of the vectors $ \vec{v_1} = \left(2,~-5\right) $ and $ \vec{v_2} = \left(3,~4\right) $ .	2
739	Determine whether the vectors $ \vec{v_1} = \left(5,~1\right) $ and $ \vec{v_2} = \left(3,~-2\right) $ are linearly independent or dependent.	2
740	Find the angle between vectors $ \left(1,~1,~1\right)$ and $\left(-2,~1,~1\right)$.	2
741	Find the sum of the vectors $ \vec{v_1} = \left(-\dfrac{ 1 }{ 2 },~\dfrac{ 2 }{ 7 }\right) $ and $ \vec{v_2} = \left(6,~23\right) $ .	2
742	Calculate the cross product of the vectors $ \vec{v_1} = \left(1,~1,~1\right) $ and $ \vec{v_2} = \left(-2,~1,~1\right) $ .	2
743	Find the sum of the vectors $ \vec{v_1} = \left(-\dfrac{ 1 }{ 7 },~\dfrac{ 2 }{ 7 }\right) $ and $ \vec{v_2} = \left(6,~23\right) $ .	2
744	Calculate the dot product of the vectors $ \vec{v_1} = \left(2,~-3,~1\right) $ and $ \vec{v_2} = \left(2,~2,~2\right) $ .	2
745	Find the projection of the vector $ \vec{v_1} = \left(-4,~-1,~0\right) $ on the vector $ \vec{v_2} = \left(1,~3,~-2\right) $.	2
746	Calculate the cross product of the vectors $ \vec{v_1} = \left(3,~-1,~1\right) $ and $ \vec{v_2} = \left(0,~-2,~2\right) $ .	2
747	Find the sum of the vectors $ \vec{v_1} = \left(1,~2\right) $ and $ \vec{v_2} = \left(1,~2\right) $ .	2
748	Find the sum of the vectors $ \vec{v_1} = \left(6,~3\right) $ and $ \vec{v_2} = \left(7,~-15\right) $ .	2
749	Find the angle between vectors $ \left(2,~3\right)$ and $\left(-3,~-2\right)$.	2
750	Find the difference of the vectors $ \vec{v_1} = \left(9,~-7\right) $ and $ \vec{v_2} = \left(8,~3\right) $ .	2