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)

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