Question

Find $|\overrightarrow{a}-\overrightarrow{b}|$, if two vectors $\overrightarrow{a}$ and $\overrightarrow{b}$ are such that $|\overrightarrow{a}|=2$, $|\overrightarrow{b}|=3$ and $\overrightarrow{a}.\overrightarrow{b}=4$

• A. $\sqrt{3}$
• B. $\sqrt{7}$
• C. $\sqrt{21}$
• D. $\sqrt{5}$

Answer 1

The correct option is D $\sqrt{5}$

Given, $|\overrightarrow{a}|=2$, $|\overrightarrow{b}|=3$ and $\overrightarrow{a}.\overrightarrow{b}=4$
We have,
${|\overrightarrow{a}-\overrightarrow{b}|}^2={|\overrightarrow{a}|}^2-2(\overrightarrow{a}.\overrightarrow{b})+{|\overrightarrow{b}|}^2$
$\Rightarrow {|\overrightarrow{a}-\overrightarrow{b}|}^2=2^2-2\times 4+3^2=5$
$\Rightarrow |\overrightarrow{a}-\overrightarrow{b}|=\sqrt{5}$