What are the ways 3 planes in $ℝ^3$ intersect? Will they be able to form points, lines, or planes?
In my opinion, the planes can only form points and lines, could someone give any counterexamples? 
 A: 1) The three planes can be parallel.  And not intersect at all.
If two planes intersect the intersection will be a line.
2) Two planes can be parallel and the third plane intersects each.  The third intersects each at a line.  These to lines are parallel and co-planer.
3) All planes intersect at a line and the third intersects the two on the same line (like pages in an open book intersecting at the spine).
4) The two planes intersect and a line.  The third intersect each at a parallel angle to insect at second and third parallel line.  The planes will from a triangular cylinder, with each pair of planes intersecting at a line.  These three lines are mutually parallel and non planar.
5) General case. Two planes intersect. A third intersects obliquely and the three intersect at a point.  Each pair of planes intersect at a line.  The three lines are neither coplanar nor parallel and the three lines intersect at the point where the three planes do.
A: Two distinct planes intersect in a line or not at all (prove this!). The line can intersect a third plane in either a line or a single point (prove this!). It's easy to construct examples where each of these cases can happen.
Now if two or more of the planes coincide, there's one more case.
