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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|
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B
tan1(Q/P)
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C
tan1(P/Q)
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D
zero
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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 correct

Physics

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