Consider the plane with general equation 3x+y+z=1 and the plane with vector equation (x, y, z)=s(1, -1, -2) + t(1, -2 -1) where s and t are real numbers. Describe the intersection of these two planes.
I started by substituting the parametric equations into the general equation and got 0=9. Does that imply the planes are parallel and hence do not intersect?