Question

# What is the angle between $$\vec {P}$$ and the resultant of $$(\vec {P}+\vec {Q})$$ and $$(\vec {P}-\vec {Q})$$?

A
tan1|(PQ)||P+Q|
B
tan1(Q/P)
C
tan1(P/Q)
D
zero

Solution

## The correct option is D zero$$\textbf{Step 1: Resultant Calculation}$$Let the resultant be $$\vec{R}$$$$\therefore \vec {R} = (\vec {P} + \vec {Q}) + (\vec {P} - \vec {Q})$$$$\Rightarrow$$ $$\vec {R} = 2\vec {P}$$       $$....(1)$$$$\textbf{Step 2: Angle between }\vec{R }\textbf{ and }\vec{P}$$From $$(1)$$ we can say that, $$\vec {R}$$ is in same direction along $$\vec {P}$$ with twice its magnitude. Thus,$$\vec{R}$$ and $$\vec{P}$$ are parallel.Therefore, the angle between $$\vec{R}$$ and $$\vec{P}$$ is zero.Hence, Option $$D$$ is correctPhysics

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