Thread: Intersection of planes in three-space?

y = z is a PLANE in 3D space, not a line.

Surely you can tell me what graph the intersection of two planes gives...

Originally Posted by AFireInside

Describe the shape of the intersection of the plane z= -3 and the plane y=z in three-space.

Well, z= -3 would be a horizontal plane 3 units down the z-axis.
Y=z is an infinite line with x being any value in the y-z plane.
I'm not sure at what line they intersect. I know z must be -3.
Would y be any value, since both z=-3 and y=z extend indefinitely along the y-axis? And would x have to be 0?
Any feedback would be appreciated.

Nope. The intersection line of the two planes is characterized by z=-3 AND y=z (since you're on both planes simultaneously).

So the intersection line must have y=z=-3. The x-value of the intersection line is not constrained.

Being the line or equivalently



we can describe the "shape" of as the line passing trough and parallel to the axis.