Question

Let $\overrightarrow{a}$ and $\overrightarrow{b}$ be two unit vectors such that angle between them is $60{}^{\circ }$ . Then $|\overrightarrow{a}-\overrightarrow{b}|$ is equal to:

• A. $\sqrt{5}$
• B. $\sqrt{3}$
• C. $0$
• D. $1$
• E. $\sqrt{2}$

Answer 1

Answer: (D)

$|\overrightarrow{a}-\overrightarrow{b}{|}^2=|\overrightarrow{a}{|}^2+|\overrightarrow{b}{|}^2-2|\overrightarrow{a}||\overrightarrow{b}|\cos \theta$ $\Rightarrow$ $|\overrightarrow{a}-\overrightarrow{b}{|}^2=1+1-2\cos 60{}^{\circ }$ $=2-1$ $\Rightarrow$ $|\overrightarrow{a}-\overrightarrow{b}|=1$