Describing the intersection of two planes 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?

As a test to see if the planes are parallel you can calculate the normalvectors for the planes {n1, n2}.
If $abs\left (\frac{(n1\cdot n2)}{\left | n1 \right |*\left | n2 \right |}  \right )==1$ the planes are parallel.
