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Math Help - orthogonal vectors point of intersection

  1. #1
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    Smile orthogonal vectors point of intersection

    Hello,

    Hello,
    I have two points p and q. i need to find point r which is defined by the intersection of the vectors pr and rq. the vectors are orthogonal, so that <pr,qr> = 0


    how can i get the point r ? How can I define my lines so i can make pl1 = ql2
    Last edited by thesys; December 23rd 2009 at 10:24 AM. Reason: error on dot product
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  2. #2
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    Hello, thesys!

    If I understand the problem, there is an infinite number of answers.


    I have two points P and Q.
    i need to find point R, defined by the intersection of \overrightarrow{PR} and \overrightarrow{QR}.

    The vectors are orthogonal, so that: . \overrightarrow{PR}\cdot\overrightarrow{QR} \:=\:0

    How can i get the point R ?
    Code:
                  * * *     R
              *           o
            *          *    *
           *       *         *
                *
          *  *                *
        P o - - - - * - - - - o Q

    We have a semicircle with diameter PQ.

    Let R be any point on the semicircle.
    Draw chords PR and QR.

    Then: . PR \perp QR

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  3. #3
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    Quote Originally Posted by Soroban View Post
    Hello, thesys!

    If I understand the problem, there is an infinite number of answers.


    Code:
                  * * *     R
              *           o
            *          *    *
           *       *         *
                *
          *  *                *
        P o - - - - * - - - - o Q

    We have a semicircle with diameter PQ.

    Let R be any point on the semicircle.
    Draw chords PR and QR.

    Then: . PR \perp QR

    Thanks for your reply!

    I mean that the points are like this:
    *r------*p------- |
    |
    |
    *q
    Last edited by thesys; December 23rd 2009 at 11:06 AM.
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  4. #4
    MHF Contributor

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    Yes, I am sure Soroban understood what "orthogonal" meant!

    And his answer is still true. Take any line through point p, except for the single line through both p and h, and there exists a line through q perpendicular to that line. There are an infinite number of possible lines through p and so an infinite number of points "r" at which lines (vectors) through p and q are orthogonal.
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