Question

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

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

Answer 1

Answer: (D)

$1$

We know that, $|\overrightarrow{a}-\overrightarrow{b}{|}^2=|\overrightarrow{a}{|}^2+|\overrightarrow{b}{|}^2-2|\overrightarrow{a}|\cdot |\overrightarrow{b}|\cos \theta$
Here, $\theta ={60}^o$
$\therefore |\overrightarrow{a}-\overrightarrow{b}{|}^2=1+1-2\cos {60}^o=2-1$
$\Rightarrow |\overrightarrow{a}-\overrightarrow{b}|=1$