Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

    User Avatar
    Staff Emeritus
    Science Advisor

    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.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Area of a triangle in 3 space using cross product
  1. Cross Product (Replies: 6)

  2. Cross product (Replies: 2)

Loading...