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Point on plane closest to point in R3

  1. Sep 6, 2010 #1
    1. The problem statement, all variables and given/known data

    Let P1 be the plane passing through the point A(5,-6,7) parallel to the xy-plane. Write down the coordinates of the point D on P1 which is closest to C(1,3,4).

    2. Relevant equations

    None.

    3. The attempt at a solution

    I am not sure how to attempt this problem. I tried sketching a diagram (attached), but didnt know what else to do.
     

    Attached Files:

  2. jcsd
  3. Sep 6, 2010 #2
    Have you tried deriving the equation of the plane P1 ?

    The equation of a plane is given as follows
    [tex] a(x-x_{0}) + b(y-y_{0}) +c(z-z_{0}) =0[/tex]
    (a,b,c) is a normal vector to the plane.

    It turns out that the distance between a point and a plane is shortest when the point is orthogonal to the plane.
     
  4. Sep 7, 2010 #3

    hunt_mat

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    Homework Helper

    It's a trick question. You know that the shortest distance from a point to a plane is in the normal direction to that plane. what is the normal to the plane they defined?
     
  5. Sep 7, 2010 #4
    Thanks, I figured it out D(1,3,7) :)
     
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