If the foot of the perpendicular from point $(4,3,8)$ on the line $\mathrm{L}_1: \frac{\mathrm{x}-\mathrm{a}}{\ell}=\frac{\mathrm{y}-2}{3}=\frac{\mathrm{z}-\mathrm{b}}{4}, \ell \neq 0$ is $(3,5$, 7), then the shortest distance between the line $\mathrm{L}_1$ and line $\mathrm{L}_2: \frac{\mathrm{x}-2}{3}=\frac{\mathrm{y}-4}{4}=\frac{\mathrm{z}-5}{5}$ is equal to :