# Distance between two parallel planes

• Nov 13th 2009, 10:08 AM
knuckles1234
Distance between two parallel planes
Find the shortest distance between the following two parallel planes:
x -2y -2z -12 = 0
and
x -2y -2z -6 = 0 .
• Nov 13th 2009, 10:16 AM
Plato
Quote:

Originally Posted by knuckles1234
Find the shortest distance between the following two parallel planes:
x -2y -2z -12 = 0
and
x -2y -2z -6 = 0 .

Given a point $P:(p,q)$ and a line $\ell:Ax+By+C=0$ then the distance between the point and the line is $\frac{|pA+qB+C|}{\sqrt{A^2+B^2}}$.

Take any point on one of the lines and find the distance to the other line.
• Nov 13th 2009, 10:18 AM
galactus
To find the distance between two planes, use the formula:

$D=\frac{|ax_{0}+by_{0}+cz_{0}+d|}{\sqrt{a^{2}+b^{2 }+c^{2}}}$

This is the formula for the distance between a point and a plane. To find the distance between the planes, choose an arbitrary point on one of the planes. Set y=z=0 in x-2y-2z-12=0 and solve for x. Then, use that as your point.