Question

If $a$ and $b$ be two unit vectors such that angle between them is $60°$. Then, $|a-b|$ is equal to?

• A. $\surd 5$
• B. $\surd 3$
• C. $0$
• D. $1$

Answer 1

The correct option is D

$1$

Explanation for the correct option:

Find the value of $|a-b|$:

Given, $\theta =60°$

As we know, $\mathbf{|}\mathit{a}\mathbf{-}\mathit{b}{\mathbf{|}}^{\mathbf{2}}\mathbf{}\mathbf{=}\mathbf{}\mathbf{|}\mathit{a}{\mathbf{|}}^{\mathbf{2}}\mathbf{+}\mathbf{|}\mathit{b}{\mathbf{|}}^{\mathbf{2}}\mathbf{-}\mathbf{2}\mathbf{|}\mathit{a}\mathbf{|}\mathbf{}\mathbf{|}\mathit{b}\mathbf{|}\mathbf{}\mathit{c}\mathit{o}\mathit{s}\mathit{\theta }$

$\begin{array}{rcl}\therefore |a-b{|}^2& =& |a{|}^2+|b{|}^2-2\left|a\right|\left|b\right|\cos 60°\\ & =& 1+1-2\times \frac{1}{2}\\ & =& 2-1\\ & =& 1\end{array}$

Hence, Option ‘D’ is Correct.