If $P$ is the point of intersection of the line joining the points $Q(2,3,5)\:\:and\:\:R(1,-1,4)$ with the plane $5x-4y-z-1=0$. If $S$ is foot of $\perp$ drawn from the point $T(2,1,4)$ to the line $QR$, then the length of segment $\overrightarrow {PS}$ = ?

Question

$\begin{array}{1 1} (a)\:\large\frac{1}{\sqrt 2}\:\:\:\qquad\:(b)\:\sqrt 2\:\:\:\qquad\:(c)\:2\:\:\:\qquad\:(d)\:2\sqrt 2. \end{array}$