The line \({{l}_{3}}\) passes through \(B(3,-4,4)\) and is parallel to \({{l}_{1}}:\mathbf{r}=\left( \begin{matrix} 1 \\ -5 \\ 2 \end{matrix} \right)+\lambda \left( \begin{matrix}14 \\ -2 \\5 \end{matrix} \right);\lambda \in \mathbb{R}\).
Find the perpendicular distance between \({{l}_{1}}\) and \({{l}_{3}}\).
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