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Math Help - Distance from Point to Plane

  1. #1
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    Distance from Point to Plane

    Without using distance formula, find the distance from the point (0,0,1) to the plane \;4y\;+\;3z\;=\;-12\;

    i dont have any idea about how to solve. :S
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  2. #2
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    Quote Originally Posted by Lafexlos View Post
    Without using distance formula, find the distance from the point (0,0,1) to the plane \;4y\;+\;3z\;=\;-12\;

    i dont have any idea about how to solve. :S
    (0,0,-4) is clearly on the plane and (0,4/5,3/5) is the unit norm of the plane.

    So |((0,0,1)-(0,0,-4)) \cdot (0,4/5,3/5)| = 3
    is the length of the projection of the segment from (0,0,-4) to (0,0,1) onto the norm of the plane,
    thus is the distance between (0,0,1) to the plane.
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  3. #3
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    Almost i get it but why are you dot producted with normal vector?
    Edit: Ok. i get it now. thx for help. =)
    Last edited by Lafexlos; April 1st 2010 at 12:02 AM.
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