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)

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