If the distance of the point $P(1,-2,1)$ from the plane $x+2y-2z=a$, where $a>0,$ is $5$, then the foot of the $\perp$ from $P$ to this plane is ?

Question

$\begin{array}{1 1}\:(a)\:\:\big(\large\frac{8}{3},\frac{4}{3},-\frac{7}{3}\big)\:\:\:\qquad\:\:(b)\:\:\big(\large\frac{4}{3},-\frac{4}{3},-\frac{1}{3}\big)\:\:\:\qquad\:\:(c)\:\:\big(\large\frac{1}{3},\frac{2}{3},-\frac{10}{3}\big)\:\:\qquad\:\:(d)\:\:\big(\large\frac{2}{3},-\frac{1}{3},-\frac{5}{3}\big) \end{array} $