Question

The angle between two vectors $A$ and $B$ is $\theta$ . Vector $R$ is the resultant of the two vectors. If $R$ makes an angle $\frac{\theta }{2}$ with $A$ , then

• A. $A=2B$
• B. $A=\frac{B}{2}$
• C. $A=B$
• D. $AB=1$

Answer 1

Answer: (C)

The angle $\alpha$ which the resultant $R$ makes with A is given by
$\tan \alpha =\frac{B\sin \theta }{A+B\cos \theta }$
or $\frac{\sin (\theta /2)}{\cos (\theta /2)}=\frac{2B\sin (\theta /2)\cos (\theta /2)}{A+B\cos \theta }$
which gives $A+B\cos \theta =2B{\cos }^2\left(\frac{\theta }{2}\right)$
or $A+B\left[2{\cos }^2\left(\frac{\theta }{2}\right)-1\right]=2B{\cos }^2\left(\frac{\theta }{2}\right)$
$A=B$