The equation of the plane containing the line $x-y+z=0=x+y+z-2$ and which is farthest from origin is

${\pi }_1+\lambda {\pi }_2=0\text{ R.D }=\frac{\left|2\lambda \right|}{\sqrt{3{\lambda }^2+2\lambda +3}}$

$\text{ Let }f\left(\lambda \right)=\frac{{\lambda }^2}{3{\lambda }^2+2\lambda +3}\Rightarrow f^{\mathrm{\prime }}\left(\lambda \right)=\frac{2\lambda (\lambda +3)}{{\left(3{\lambda }^2+2\lambda +3\right)}^2}$

$\lambda =-3\text{ gives maximum }$

$\therefore \text{ Required plane is }{\pi }_1-3{\pi }_2=0\Rightarrow x+2y+z-2=0$