1. Write the two given vectors

The vectors are: $\vec{A}=2\vec{Q}+2\vec{P}$ $\vec{B}=2\vec{Q}-2\vec{P}$

2. Find their resultant

The resultant of two vectors is their sum: $\vec{R}=\vec{A}+\vec{B}$

Substituting: $\vec{R}=(2\vec{Q}+2\vec{P})+(2\vec{Q}-2\vec{P})$

Now simplify: $\vec{R}=2\vec{Q}+2\vec{P}+2\vec{Q}-2\vec{P}$ $\vec{R}=4\vec{Q}$

3. Compare the direction of $\vec{R}$ with $\vec{Q}$

Since $\vec{R}=4\vec{Q}$ it means the resultant is a positive scalar multiple of $\vec{Q}$. Therefore, $\vec{R}$ is in the same direction as $\vec{Q}$.

Hence, the angle between $\vec{Q}$ and $\vec{R}$ is: $0^\circ$

4. Check options

• A: $\tan^{-1}(P/Q)$ — incorrect
• B: $0^\circ$ — correct
• C: expression given is not the required angle — incorrect
• D: $\tan^{-1}(2Q/P)$ — incorrect

Therefore, the correct option is: $\boxed{B}$