Results 1 to 3 of 3

Thread: Distance between two parallel planes

  1. #1
    Newbie
    Joined
    Nov 2009
    Posts
    5

    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 .
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    21,743
    Thanks
    2814
    Awards
    1
    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 $\displaystyle Pp,q)$ and a line $\displaystyle \ell:Ax+By+C=0$ then the distance between the point and the line is $\displaystyle \frac{|pA+qB+C|}{\sqrt{A^2+B^2}}$.

    Take any point on one of the lines and find the distance to the other line.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Eater of Worlds
    galactus's Avatar
    Joined
    Jul 2006
    From
    Chaneysville, PA
    Posts
    3,002
    Thanks
    1
    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.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. How do I know if two planes are parallel?
    Posted in the Advanced Algebra Forum
    Replies: 3
    Last Post: Oct 15th 2011, 08:08 AM
  2. Parallel planes and intersecting planes
    Posted in the Calculus Forum
    Replies: 2
    Last Post: Jun 8th 2010, 08:25 AM
  3. Replies: 2
    Last Post: Jun 4th 2010, 05:00 AM
  4. Distance between the given parallel planes:
    Posted in the Calculus Forum
    Replies: 4
    Last Post: May 28th 2010, 02:30 AM
  5. [SOLVED] Distance between Parallel Planes
    Posted in the Calculus Forum
    Replies: 3
    Last Post: Sep 26th 2009, 04:12 PM

Search Tags


/mathhelpforum @mathhelpforum