intersections

• Apr 27th 2008, 11:02 PM
federer
intersections
Suppose P and Q are two distinct planes in R³. What sort of set could their intersection be?
Answer in words and give a sketch to show the possibilities.
• Apr 28th 2008, 12:09 AM
CaptainBlack
Quote:

Originally Posted by federer
Suppose P and Q are two distinct planes in R³. What sort of set could their intersection be?
Answer in words and give a sketch to show the possibilities.

If they are parallel their intersection is the null set.

If they are not parallel their intersection is a straight line.

RonL
• Apr 28th 2008, 01:20 AM
Isomorphism
Quote:

Originally Posted by federer
Suppose P and Q are two distinct planes in R³. What sort of set could their intersection be?
Answer in words and give a sketch to show the possibilities.

Another point of view:
Two planes in R^3, correspond to 2 linear equations in three variables.
Now what can you tell about the solution to this system.

Can it have a unique solution?Can it have infinitely many solutions? Can it have no solutions?