Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Distance from a point to a plane

  1. Oct 1, 2011 #1
    I am trying to show that the point in the plane ax+by+cz=d closest to the origin is
    P(ad/D^2, bd/D^2, cd/D^2) where D^2=a^2 + b^2 + c^2. How do I approach this? I tried using partial derivatives but got too complex after a while. Thanks
     
  2. jcsd
  3. Oct 1, 2011 #2

    mathman

    User Avatar
    Science Advisor
    Gold Member

    The vector (a,b,c) is perpendicular to the plane. Therefore the line given by parametric form (at,bt,ct) passes through the origin and intersects the plane at the point closest to the origin. Simply calculate the distance after finding t.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook