Consider the plane  $\Pi :x-2y+3z=31$  and the line  $\mathcal{l}$  given in parametric form by
$\mathcal{l}:\{\begin{array}{l}x=-t+2\\ y=t-1\\ z=-2t+3\text{\hspace{1em} for all }t\in ℝ\end{array},$
then which of the following option(s) is / are true
 

Parametric form of the line ${\mathcal{l}}^{*}$   such that ${\mathcal{l}}^{*}$   is the reflection of  $\mathcal{l}$ about $\pi$  .
 ${\mathcal{l}}^{*}:\{\begin{array}{l}x=2t+4\\ y=-11t-3\\ z=7t+13\text{\hspace{1em} for all }t\in ℝ.\end{array}$
 

Parametric form of the line  $\widehat{\mathcal{l}}$  such that $\widehat{\mathcal{l}}$  is the orthogonal projection of $\mathcal{l}$  onto  $\pi$  is 
 $\widehat{\mathcal{l}}:\{\begin{array}{l}x=-5t+4\\ y=-4t-3\\ z=-t+7\text{\hspace{1em} for all }t\in ℝ.\end{array}$
 

Point on   $\mathcal{l}$  ,for which the shortest distance between the point and the plane $\pi$   is  $\frac{3}{\sqrt{14}}$ , can be  $\left(\frac{13}{3},-\frac{10}{3},\frac{23}{3}\right)$ 
 

Point on $\mathcal{l}$ ,for which the shortest distance between the point and the plane $\pi$ is   $\frac{3}{\sqrt{14}}$ , can be   $\left(\frac{11}{3},-\frac{8}{3},\frac{19}{3}\right)$