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Area of a triangle in 3 space using cross product

  1. Oct 17, 2008 #1
    Hi all, I have a general question.

    When calculating the area of a triangle in 3 space, one applies the formula

    1/2||axb||. Given three vertices, a,b,c....does it matter which vectors we choose to use (ab, bc, ac) as our a b vectors?

    Thanks!
     
  2. jcsd
  3. Oct 17, 2008 #2

    HallsofIvy

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    First, because of the norm, it does not matter which is a and which is b: that is (1/2)||axb||= (1/2)||bxa||. That is, order doesn't matter. Now if a, b, and c are vectors forming a triangle, then c= a+ b so (1/2)||axc||= (1/2)||ax(a+b||= (1/2)||axa+ ab|= (1/2)||axb|| because axa= 0. In other words, all combinations give the same result.
     
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