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Math Help - Distance from a Plane

  1. #1
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    Distance from a Plane

    Hi all, I'm having a bit of trouble with this linear algebra question, and would really appreciate some help:

    Find the distance from P(3,0,-1) to the plane P described by the equation 4x + 2y -z = 6.
    Find the closest point to P which lies on the Plane P.

    I've got the distance -- that's (the square root of 21)/3.
    But I keep getting the coordinates of the closest point wrong.
    I get (4/3, 2/3, -1/3), but the answer's apparently (5/3, -2/3, -2/3)

    What am I doing wrong?
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  2. #2
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    Quote Originally Posted by rorosingsong View Post
    Find the distance from P(3,0,-1) to the plane P described by the equation 4x + 2y -z = 6.
    Find the closest point to P which lies on the Plane P.
    If \mathif{N} is the normal to the plane the find where the line \mathif{P}+t\mathif{N} intersects the plane.
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