Question

If $| a |=| b |=| a - b |=1 .$ Then angle between $a$ and $b$ is

• A. $\frac{\pi}{6}$
• B. $\frac{\pi}{4}$
• C. $\frac{\pi}{3}$
• D. $\frac{\pi}{2}$
• E. $\frac{\pi}{8}$

Answer 1

Answer: (C)

We know that
$| a - b |^{2}=( a - b ) \cdot( a - b )$
$\Rightarrow ( l )^{2}=| a |^{2}+| b |^{2}-2 a \cdot b \,\,\,[\because| a |-| b |=1]$
$\Rightarrow l = l + l -2| a || b | \cos \theta$
$[\because| a |=| b |=1$ and $\theta$ is angle between $a$ and $b ]$
$\Rightarrow 1=2-2 \cos \theta$
$\Rightarrow \cos \theta=\frac{1}{2}$
$\Rightarrow \theta=\frac{\pi}{3} \,\,\,\left[\because \cos \frac{\pi}{3}=\frac{1}{2}\right]$