Question

If $\theta$ be the angle between the unit vectors a and b, then $\cos \frac{\theta }{2}$ is equal to

• A. $\frac{1}{2}|a-b|$
• B. $\frac{1}{2}|a+b|$
• C. $\frac{|a-b|}{|a+b|}$
• D. $\frac{|a+b|}{|a-b|}$

Answer 1

Answer: (B)

$(a+b)\cdot (a+b)=|a{|}^2+\left|b^2\right|+2a\cdot b$
$=1+1+2(1)(1)\cos \theta =2+2\cos \theta$
$\Rightarrow |a+b{|}^2=2\cdot 2\cos \frac{\theta }{2}$
$\Rightarrow \cos \frac{\theta }{2}=\frac{1}{2}|a+b|$