Question

The resultant of two vectors $\overrightarrow{P}$ and $\overrightarrow{Q}$ is $\overrightarrow{R}$. If $Q$ is doubled; the new resultant is perpendicular to P, then R equals to:

• A. $P$
• B. $Q$
• C. $P+Q$
• D. $P-Q$

Answer 1

Answer: (B)

$\tan \beta =\frac{B\sin \theta }{A+B\cos \theta }$
$\tan 90^{\circ }=\frac{Q\sin \theta }{P+2Q\cos \theta }$
$\infty =\frac{Q\sin \theta }{P+2Q\cos \theta }$
$\Rightarrow \frac{1}{0}=\frac{Q\sin \theta }{P+2Q\cos \theta }$
$P+2Q\cos \theta \Rightarrow \cos \theta =\frac{-P}{2Q}$
$R=\sqrt{(P{)}^2+(Q{)}^2+2PQ\times \cos \theta }=Q$