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Addition of vectors with triangle vertices

  1. Jan 22, 2012 #1
    1. The problem statement, all variables and given/known data

    If A, B, and C are the vertices of a triangle, find the following.
    (A→B) + (B→C) + (C→A)


    The answer has to be given like this:

    _____ i + _____ j

    2. Relevant equations (I think?)
    a+b=b+a
    a+(b+c)=(a+b)+c
    a+0=a
    a+(-a)=0
    c(a+b)=ca+cb
    (c+d)a=ca+da
    (cd)a=c(da)
    1a=a

    3. The attempt at a solution

    I'm not even sure what kind of solution this should look like. My best guess would be
    <A+B+C>i + <A+B+C>j
    Any better, more sensible ideas? Thanks!
     
  2. jcsd
  3. Jan 22, 2012 #2

    Dick

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    The vector connecting A to B is given by the vector (B-A), where B and A are the coordinates of the points. Add up all three terms. What do you get?
     
  4. Jan 22, 2012 #3
    Oh okay, so it all cancels out and comes to 0. That makes sense. Thank you!
     
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