Planes between Planes

Date: 04/02/2001 at 07:00:54
From: Nikila
Subject: Planes

How can I find if a plane lies between two other planes?

Thanks in advance.

Date: 04/02/2001 at 13:03:21
From: Doctor Rob
Subject: Re: Planes

Thanks for writing to Ask Dr. Math, Nikila.

If the planes aren't all parallel, your question is not meaningful:  
two nonparallel planes intersect, so parts of each plane will lie on 
either side of the other. Thus I must assume that the three planes are 
parallel.

Write the equations of all three planes in the form

   A*x + B*y + C*z = D(i),  i = 1, 2, 3.

You can do this using the same values of A, B, and C for all
three.  Then the plane with the middle of the three values D(i)
will lie between the other two.

- Doctor Rob, The Math Forum
  http://mathforum.org/dr.math/