Question

The resultant of two vectors $ \overrightarrow{P} $ and $ \overrightarrow{Q} $ is $ \overrightarrow{R} $ . If the magnitude of $ \overrightarrow{Q} $ is doubled, the new resultant becomes perpendicular to $ \overrightarrow{P} $ . Then the magnitude of $ \overrightarrow{R} $ is

• A. $ P+Q $
• B. $ Q $
• C. $ P $
• D. $ \frac{P+Q}{2} $
• E. $ P-Q $

Answer 1

Answer: (B)

In first case
$ R=\sqrt{{{P}^{2}}+{{Q}^{2}}+2PQ\cos \theta } $ ...(i)
where $ \theta $ is the angle between P and Q. In second case,
$ (\overrightarrow{P}+2\overrightarrow{Q}).\overrightarrow{P}=0 $ or $ \overrightarrow{P}\overrightarrow{P}+2(\overrightarrow{Q}.\overrightarrow{P})=0 $
or $ {{P}^{2}}+0=0 $
or $ P=0 $ Putting $ P=0 $ in Eq. (i),
we get $ R=\sqrt{0+{{Q}^{2}}+0}=Q $