How can you determine how two planes would interact?
You can use matrices and row elimination, or (equivalently) solve simultaneously.[br]Using the normals, consider whether any planes are parallel or coincident to determine the number of possible solutions for the system of equations.
If they intersect, how can you find the equation of the line of intersection?
Three Planes
How many different ways can 3 planes interact?
How can you determine how three planes would interact?
You can use matrices and row elimination, or (equivalently) solve simultaneously.[br]Using the normals, consider whether any planes are parallel or coincident to determine the number of possible solutions for the system of equations.
If they intersect, how can you find the equation of the line of intersection?
If they don't intersect at the same line, but each pair of planes intersect on 3 different lines, what do these lines have in common?
All the lines are parallel, and they go in the direction of the cross product of the normals of each of the planes.