Question

Given that P = 12, Q = 5 and R = 13 also $\overrightarrow{P}+\overrightarrow{Q}=\overrightarrow{R}$, then the angle between $\overrightarrow{P}$ and $\overrightarrow{Q}$ will be :

• A. $\pi$
• B. $\frac{\pi }{2}$
  
• C. zero
• D. $\frac{\pi }{4}$
  

Answer 1

Answer: (B)

$\frac{\pi }{2}$

Consider the problem

Let $x$ is the angle between $P$ and $Q$ .

$\overrightarrow{R}=\overrightarrow{P}+\overrightarrow{Q}$

$\therefore 13=\sqrt{(5^2+{12}^2+(2\times 5\times 12\times Cosx\left)\right)}$ [$\because |\overrightarrow{a}+\overrightarrow{b}|=\sqrt{a^2+b^2+2ab\cos \theta }$ ]

$\Rightarrow 169=169+120\cos x$

$\Rightarrow 0=120\cos x$

$\Rightarrow \cos x=0$

$\therefore x={90}^{\circ }=\frac{\pi }{2}$

Hence option $B$ is the correct answer.