In R^3 (3-D space), what does does the region xyz=0 represent?

Question

Best description of this region will receive best answer.

Answer 1

It simultaneously represents all the three otherwise separate perpendicular planes:

x = 0, y = 0, z = 0,

intersecting one another through the origin (x, y, z) = (0, 0, 0), all at once.

(It's a bit like an unbounded 3-dimensional analogue of the kind of cardboard dividers you may have sometimes seen in cases of wine. Come to think of it, it's late on a Friday night, and I'll go and drink to that.)

Live long and prosper.

Answer 2

I'm not in any math that high, but, given the fact that in xyz = 0, either x, y, or z (or two or all three) would have to equal zero. from there, maybe it means it would be a place with less than three dimensions (if y = 0, then only the plane of x and z would be there). I don't know though. just adding my idea.

Answer 3

The expression xyz will be zero if either x is zero (the y-z plane), or y is zero (the x-z plane), or z is zero (the x-y plane). The region represented by the equation is the three planes. Any point in any of the planes satisfies the equation.

Answer 4

Think of it as graphing that you did in middle and high school math classes. X and Y are the height and width of what you are talking about. The only difference is Z is used to show 3-D objects by being the axis of deepth.

Answer 5

It consists of X-Y plane,Y-Z plane and X-Z plane.