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Math Help - Simple vector question

  1. #1
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    Simple vector question

    Given A(1,7) and B(8,3). C lies on OB where O is the origin. If vector OA + BA + CA is perpendicular to vector OB, find the coordinates of C.

    The answer i get is C=(112/73 , 42/73) but the answer given is (-71/2 , 195/7). What answer do you get?

    Maybe i should show my steps and someone can point out my mistake for me...

    C lies on OB, so C = k(8,3)

    BA = OA-OB = (-7,4)

    CA= OA-OC = (1-8k, 7-3k)

    OA + BA + CA = (-5-8k, 18-3k)

    OA + BA + CA is perpendicular to vector OB, so

    OA + BA + CA . OB = 0

    (-5-8k, 18-3k) . (8,3)=0

    -8(5+8k) + 3(18-3k) = 0

    k= 14/73

    So C = k(8,3) = 14/73 . (8,3)

    Which step have i go wrong?
    Last edited by MichaelLight; October 4th 2011 at 12:42 AM.
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  2. #2
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    Opalg's Avatar
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    Re: Simple vector question

    The given answer does not even lie on the line OB. So either you have misread the question, or the book is wrong.
    Last edited by Opalg; October 5th 2011 at 12:38 AM. Reason: corrected typo
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