Question

The angle between vector $\vec{Q}$ and the resultant of $(2\vec{Q} + 2\vec{P})$ and $(2\vec{Q} - 2\vec{P})$ is:

• A. $0^\circ$
• B. $\tan^{-1}\left(\frac{2\vec{Q} - 2\vec{P}}{2\vec{Q} + 2\vec{P}}\right)$
• C. $\tan^{-1}\left(\frac{P}{Q}\right)$
• D. $\tan^{-1}\left(\frac{2Q}{P}\right)$

Answer 1

Answer: (A)

$0^\circ$

Answer 2

The resultant vector is given by:

$\vec{R} = (2\vec{Q} + 2\vec{P}) + (2\vec{Q} - 2\vec{P}) = 4\vec{Q}$

The angle between $\vec{Q}$ and $\vec{R}$ is $0^\circ$ as they are in the same direction. Therefore, Option (1) is correct.