Question

Two vectors $\overrightarrow{a}$ and $\overrightarrow{b}$ are such that $|\overrightarrow{a}|=3,|\overrightarrow{b}|=2$ and are inclined at an angle of $\frac{\pi }{3}.$ Then $|\overrightarrow{a}-\overrightarrow{b}|$ is equal to

• A. $\sqrt{19}$
• B. $\sqrt{7}$
• C. $7$
• D. $2\sqrt{3}$

Answer 1

The correct option is B $\sqrt{7}$

$|\overrightarrow{a}-\overrightarrow{b}{|}^2$
$=|\overrightarrow{a}{|}^2+|\overrightarrow{b}{|}^2-2\overrightarrow{a}\cdot \overrightarrow{b}$
$=3^2+2^2-2\times 3\times 2\times \frac{1}{2}$
$=7$
$\therefore |\overrightarrow{a}-\overrightarrow{b}|=\sqrt{7}$