Question

If the sum of two unit vectors is a unit vector, then the magnitude to thier difference is

• A. $\sqrt{2}$ units
• B. $2$ units
• C. $\sqrt{3}$ units
• D. $\sqrt{5}$ units

Answer 1

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

Let $\overrightarrow{a}$ and $\overrightarrow{b}$ be two unit vectors.
Given, $|\overrightarrow{a}+\overrightarrow{b}|=1$
$\Rightarrow |\overrightarrow{a}{|}^2+|\overrightarrow{b}{|}^2+2\overrightarrow{a}\cdot \overrightarrow{b}=1$
$\Rightarrow \overrightarrow{a}\cdot \overrightarrow{b}=\frac{-1}{2}$

$|\overrightarrow{a}-\overrightarrow{b}{|}^2=|\overrightarrow{a}+\overrightarrow{b}{|}^2-4\overrightarrow{a}\cdot \overrightarrow{b}\Rightarrow |\overrightarrow{a}-\overrightarrow{b}|=\sqrt{1-4\times \left(\frac{-1}{2}\right)}=\sqrt{3}$