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 ---------(i)which is parallel to the given line and perpendicular to the given plane            -a+2b+3c=0 -------(ii) and      a-2b+c=0 -------(iii)From Eqs. (ii) and (iii), we get c=0,    a=2b From Eq. (i), 2b (x + 1) + by = 0 ⇒2x+y+2=0