Let $\vec a,b$ be two vectors such that $|\vec a| = 2, |\vec b| = 3,\vec a.\vec b=4$, then $|\vec a-\vec b|$ is equal to

$\sqrt{5}$

The correct answer is Option (2) → $\sqrt{5}$

Given

$|\vec a|=2,\;|\vec b|=3,\;\vec a\cdot\vec b=4$

Use formula

$|\vec a-\vec b|^{2}=|\vec a|^{2}+|\vec b|^{2}-2(\vec a\cdot\vec b)$

Substitute values

$|\vec a-\vec b|^{2}=2^{2}+3^{2}-2(4)$

$=4+9-8$

$=5$

$|\vec a-\vec b|=\sqrt{5}$