Question

If $a$ and $b$ are unit vectors and $\theta$ is the angle between them, then $a-b$ will be a unit vector if $\theta =$

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

Answer 1

The correct option is B $\frac{\pi }{3}$

$\begin{array}{c}\left|a\right|=1\\ \left|b\right|=1\\ \left|a-b\right|=1\\ \left|a-b\right|=\sqrt{{\left|a\right|}^2+{\left|b\right|}^2-2\left|a\right|\left|b\right|\cos \theta }\\ \Rightarrow 1=\sqrt{1+1-2\cos \theta }\\ \Rightarrow 1=2-2\cos \theta \\ \Rightarrow \cos \theta =\frac{1}{2}\\ \theta =\frac{\pi }{3}\end{array}$