Question

Two equal vectors have a resultant equal to either of them, then the angle between them will be

• A. ${110}^o$
• B. ${120}^o$
• C. ${60}^o$
• D. ${150}^o$

Answer 1

Answer: (B)

${120}^o$

Applying the formula:

$R^2=P^2+Q^2+2PQ\cos \alpha$

$P^2=P^2+P^2+2PP\cos \alpha$

$=2P^2+2P^2\cos \alpha =2P^2(1+\cos \alpha )$

$1+\cos \alpha =\frac{1}{2}$

$\Rightarrow 2{cos}^2\frac{\alpha }{2}=\frac{1}{2}$

$\Rightarrow {cos}^2\frac{\alpha }{2}=\frac{1}{4}$

$\Rightarrow \cos \frac{\alpha }{2}=\frac{1}{2}=\cos {60}^o$

$\Rightarrow \frac{\alpha }{2}={60}^o\Rightarrow \alpha ={120}^o$