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Math Help - Shortest distance

  1. #1
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    Shortest distance

    how do you prove that the shortest distance from a point to a line ( L) in R^3 (or any R^n) is achieved along the perpendicular line connecting A to line( L).

    thanks
    Last edited by honks; April 16th 2009 at 03:16 PM.
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  2. #2
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    On the assumption that a unique perpendicular RP from point R of line L to point P always exists, you may consider \bigtriangleup PQR, where <br />
Q is any other point on line L.
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  3. #3
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    this is an assumption
    Quote Originally Posted by Scott H View Post
    that a unique perpendicular RP from point R of line L to point P always exists
    how do we prove this though?

    i understand that i must use the dot product and it should equal zero, where the shortest distance is when the point( A) is perpendicular to the line ( L)
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  4. #4
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    proved for two-dimensional space and then saw R3..OOPS!
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