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Math Help - Distance between two parallel planes

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    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 .
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    Quote Originally Posted by knuckles1234 View Post
    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,q)" alt="Pp,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.
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  3. #3
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    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.
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