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Plane Proof

  1. May 26, 2014 #1
    1. The problem statement, all variables and given/known data

    Let A, B, C be the vertices of a triangle in the plane and let a, b, c be respectively, the midpoints of the opposite sides. Show that Aa+ Bb+ Cc = 0 (all of them have vector signs on the left).

    2. Relevant equations

    definition of plane

    3. The attempt at a solution

    Drew the picture which would look like a triangle within a triangle. The form Aa... looks most like the component equation but I don't understand how a, b, c equates to x, y, z.
  2. jcsd
  3. May 26, 2014 #2


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    You say a,b,c are midpoints of sides then you say they are vectors?? If everything is a vector what does Aa mean? And what are x,y,z? You need to state your problem more carefully.
  4. May 27, 2014 #3
    That is exactly how the problem appears as written by the professor. A, B, and C form a triangle with a, b, c as midpoints. I meant that in the equation for example Aa has a vector sign hovering over it, but I don't know how to type in that symbol.
  5. May 27, 2014 #4


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    OK, so you mean ##\vec{Aa}+\vec{Bb} +\vec {Cc} = \vec 0##. Here's a hint:$$
    \vec{Aa} = \vec{AB} +\frac 1 2 \vec{BC}$$and similarly for the other two.
  6. May 27, 2014 #5
    Got it thanks.
    Last edited: May 27, 2014
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