Describe all possible ways in which two planes (passing through origin) in R3 could intersect.

Answer 1

When two plane in R3 intersect, their intersection will be a line (just imagine the line formed by the intersection of the floor and the wall in a room). The only other possibility is if the two planes coincide, in other words, if the two planes are the same, in which case their intersection is a plane. I hope that was clear.

Answer 2

The line of the third plane has to be parallel, the third plane have to intersect as the other two planes on the same line whereas the two planes are intersected.