The equation of projection of the line $\large\frac{x-1}{2}=\frac{y-2}{1}=\frac{z-3}{3}$ on the plane $x+y+z=1$ is given by ?

Question

$\begin{array}{cc}(a)\:x+y+z-1=0=2x-y-z+3\: & (b)\:x+y+z-1=0=x-2y-z+3\: \\ (c)\:x+y+z-1=0=x-y-2z+3\: & (d)\:x+y+z-1=0=2x-y-z-3\end {array}$