Intersection of Two Planes
Given two planes:
Form a system with the equations of the planes and calculate the ranks.
r = rank of the coefficient matrix.
r'= rank of the augmented matrix.
The relationship between the two planes can be described as follows:
| Position | r | r' | |
|---|---|---|---|
| Intersecting | 2 | 2 |  |
| Parallel | 1 | 2 |  |
| Coincident | 1 | 1 |  |
Examples
State the relationship between the planes.
1. 
For intersecting planes, the intersection is a line.
2. 
Parallel planes.
3. 
Coincident planes.
