The projection of the line x+1−1=y2=z−13 on the plane x−2y+z=6 is the line of intersection of this plane with the plane

Equation of the plane through (-1, 0, 1) is a(x+1)+b(y−0)+c(z−1)=0-------iwhich is parallel to the given line and perpendicular to the given plane −a+2b+3c=0----iiand    a−2b+c=0----iiiFrom Eqs. (ii) and (iii), we get c=0,a=2b From Eq. (i) 2b(x+1)+by=0⇒2x+y+2=0