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Math Help - triangles represented using vectors

  1. #1
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    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
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    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

    M\cdot(B-A)=(A+\gamma(B-A))\cdot(B-A)=0

    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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