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

The Correct Option is A

The resultant vector is calculated as:

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

Since \(\vec{Q}\) and \(\vec{R}\) are in the same direction, the angle between them is \(0^\circ\). Thus, Option (1) is the correct choice.