# Intersection of three planes

• Oct 30th 2010, 05:41 AM
Ant
Intersection of three planes
If three planes (3 equations, 3 variables) intersect infinitely many times. (i.e. having solved 3 equations simultaneously you get two leading variables and one free variable). Does this mean that all three planes are the same plane?

I'm trying to imagine it and the only way I can picture 3 planes intersecting an infinite number of times would be if all three are actually the same plane?

Is this correct???

Thanks!
• Oct 30th 2010, 05:46 AM
Ant
Sorry, just given this some more thought I can now see that they don't have to be the same plane! Because you can have an infinite number of decimal places it means that there can be an infinite number of intersections on a finite line?

Just as there is a infinite number of points on a line segment.

Is THIS correct?? :)
• Oct 31st 2010, 01:34 PM
h2osprey
Yes, the intersection of these three planes is a line (assuming you do get two leading variables and one free variable).
• Oct 31st 2010, 06:23 PM
HallsofIvy
In other words, you can have two of the planes the same and the third plane intersecting them in a line.