# The equation of the plane passing through the line of intersection of the planes $x+2y+3z=2$ and $x-y+z=3$ and at a distance $\large\frac{2}{\sqrt 3}$ from the point $(3,1,-1)$ is
$\begin{array}{1 1} 5x-11y+z=17 \\ \sqrt 2 x+y=3 \sqrt 2 -1 \\ x+y+z= \sqrt 3 \\ x-\sqrt 2 y =1-\sqrt 2 x \end{array}$