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.
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.
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?