Understanding Intersection of Two Planes I'm trying to understand the meaning of this equation (2+s-3t, -1-2s+t, 3-t) (s,t∈R) Supposedly this is the intersection of two planes, however it seems to me that this is still an equation for a plane. Question: So does that mean that the original planes are actually just coincident? Additionally, in the z bracket, why is there no s value, and what does that mean? ~Thanks!

Your vector can be written $$\begin {pmatrix}2 \\\\-1\\\ 3 \end {pmatrix} + s \begin {pmatrix}1\\\\-2\\\ 0 \end {pmatrix} + t \begin {pmatrix}-3\\\1\\\ -1 \end {pmatrix} $$ which does represent a plane. The first vector represents a point on the plane and the other 2 vectors form a basis for the plane and different values of the parameters $s$ and $t$ take you to different points in the plane. It does not matter that $s$ does not appear in the $z$ component.