Find the shortest distance between the following two parallel planes:x -2y -2z -12 = 0

and

x -2y -2z -6 = 0 .

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- Nov 13th 2009, 09:08 AMknuckles1234Distance between two parallel planesFind the shortest distance between the following two parallel planes:x -2y -2z -12 = 0

and

x -2y -2z -6 = 0 .

- Nov 13th 2009, 09:16 AMPlato
- Nov 13th 2009, 09:18 AMgalactus
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.