Question

If $|\overrightarrow{a}|=|\overrightarrow{b}|=|\overrightarrow{a}+\overrightarrow{b}|=1,then|\overrightarrow{a}-\overrightarrow{b}|$ is equal to

• A. 1
• B. $\sqrt{2}$
• C. $\sqrt{3}$
• D. None of these
  

Answer 1

The correct option is C $\sqrt{3}$

We have,
$|\overrightarrow{a}+\overrightarrow{b}{|}^2+|\overrightarrow{a}-\overrightarrow{b}{|}^2=2(|\overrightarrow{a}{|}^2+|\overrightarrow{b}{|}^2)\Rightarrow 1+|\overrightarrow{a}-\overrightarrow{b}{|}^2=4\Rightarrow |\overrightarrow{a}-\overrightarrow{b}{|}^2=3$