Let \(\vec{a},\vec{b}\) be two vectors such that \(\left|\vec{a}\right|=2,\left|\vec{b}\right|=3\) and \(\vec{a}\cdot \vec{b}=4\) then \(\left|\vec{a}-\vec{b}\right|\) is

\(\sqrt{2}\) \(\sqrt{3}\) \(\sqrt{5}\) \(\sqrt{7}\)

\(\sqrt{5}\)

\(\begin{aligned}\left|\vec{a}-\vec{b}\right|^{2}&=|\vec{a}|^{2}+|\vec{b}|^{2}-2\vec{a}\vec{b}\\ &=4+9-8\\ &=5\\ |\vec{a}-\vec{b}&=\sqrt{5}\end{aligned}\)