If two vectors $\vec{a}$ and $\vec{b}$ are such that $|\vec{a}|=2, |\vec{b}|=3$ and $\vec{a}.\vec{b}= 4$, then $|\vec{a}-2\vec{b}|$ is :

$2\sqrt{6}$

The correct answer is Option (3) → $2\sqrt{6}$

$|\vec{a}-2\vec b|=\sqrt{(\vec{a}-2\vec b).(\vec{a}-2\vec b)}$

$=\sqrt{|\vec a|^2+4|\vec b|^2-4\vec a.\vec b}$

$=\sqrt{4+36-16}$

$=\sqrt{24}=2\sqrt{6}$