Find the shortest distance between the following two parallel planes:x -2y -2z -12 = 0
and
x -2y -2z -6 = 0 .
To find the distance between two planes, use the formula:
$\displaystyle D=\frac{|ax_{0}+by_{0}+cz_{0}+d|}{\sqrt{a^{2}+b^{2 }+c^{2}}}$
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.