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Point on plane closest to point in R3

  • Thread starter TsAmE
  • Start date
  • #1
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Homework Statement



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).

Homework Equations



None.

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.
 

Attachments

Answers and Replies

  • #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.
 
  • #3
hunt_mat
Homework Helper
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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?
 
  • #4
132
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Thanks, I figured it out D(1,3,7) :)
 

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