\[
\text{The angle between vector } \vec{Q} \text{ and the resultant of }
(2\vec{Q}+2\vec{P}) \text{ and } (2\vec{Q}-2\vec{P}) \text{ is}
\]
\[
\text{(A) }0^\circ
\qquad
\text{(B) }\tan^{-1}\left(\frac{2\vec{Q}-2\vec{P}}
{2\vec{Q}+2\vec{P}}\right)
\]
\[
\text{(C) }\tan^{-1}\left(\frac{P}{Q}\right)
\qquad
\text{(D) }\tan^{-1}\left(\frac{2Q}{P}\right)
\]
\[
\textbf{Solution:}
\]
\[
\vec{R}=(2\vec{Q}+2\vec{P})+(2\vec{Q}-2\vec{P})
\]
\[
\vec{R}=2\vec{Q}+2\vec{P}+2\vec{Q}-2\vec{P}
\]
\[
\boxed{\vec{R}=4\vec{Q}}
\]
\[
\therefore\ \text{Angle between }\vec{Q}\text{ and }\vec{R}=0^\circ
\]
\[
\boxed{\text{Correct Answer: (A)}}
\]
Abc