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Thread: triangles represented using vectors

  1. #1
    Apr 2008

    triangles represented using vectors

    Consider a triangle ABC formed by the vectors a=(2,10,25) and b=(5,4,-2) attached at the point A. I've calculated the area of the triangle as  40.5\sqrt{5} and now need to find the vector h=AM, the height of the triangle [so AM is perpendicular to BC and M lies on the line BC]. I've tried using so many different formulae to try and find h or the third side of the triangle and nothing I get seems sensible. Can someone please give me some hints or suggestions on where to start so I can work through this problem? Thanks.
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  2. #2
    MHF Contributor
    Mar 2010
    The line going through A and B is just A+\gamma(B-A), where \gamma is a real number. So  \gamma=0 gives point A and \gamma=1 gives point B.

    The altitude AM of the triangle has to be perpendicular to that line, so


    which you should be able to solve for \gamma, and then find M.

    Post again in this thread if you're still having trouble.

    - Hollywood
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