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

$\sqrt{5}$

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

We have

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

$= \vec{a} \cdot \vec{a} - \vec{a} \cdot \vec{b} - \vec{b} \cdot \vec{a} + \vec{b} \cdot \vec{b}$

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

$= (2)^2 - 2(4) + (3)^2$

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