Image of $\left(\mathrm{3,1},7\right)$ w.r.t. plane $x-y+z-3=0$ is
$\frac{x-3}{1}=\frac{y-1}{-1}=\frac{z-7}{1}=-2\frac{\left(6\right)}{3}=-4$
$x=-1,y=5,z=3$

So, image is $\left(-\mathrm{1,5},3\right)$
Equation of the plane through $P$ and parallel to $x-2y+3z=7$ is
$1\left(x+1\right)-2\left(y-5\right)+3\left(z-3\right)=0$
$x+1-2y+10+3z-9=0$
$x-2y+3z+2=0$