Find the equation of the plane through the line of intersection of the planes $x + y + z = 1$ and $2x + 3y + 4z = 5$ which is perpendicular to the plane$x -y + z = 0.$

Question

$\begin{array}{1 1} x+z+2=0 \\ x-z-2=0 \\ x-z+2=0 \\ x-y+2=0\end{array} $