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Math Help - Need some help, vector proofs

  1. #1
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    Need some help, vector proofs

    Thanks for the help
    Last edited by eekoz; May 12th 2006 at 07:54 PM.
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  2. #2
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    Quote Originally Posted by eekoz
    Okay, so I have a triagle with vertices A, B, and C.
    I know that the centroid, G, is where all the medians of the triangle intersect, and G divides the median at a 2:1 ratio
    Assuming point O is a point that's not on the triangle, how can I prove:
    OG = 1/3(OA + OB + OC) ?
    Thanks in advance!
    Hello,

    1. I've attached a diagram to demonstrate what I've calculated.

    2. You ought to know that the vector (OM_{BC})=\frac{1}{2}((OB)+(OC))

    3. You get three equations, which always describe the vector (OG):

    (OG)=(OA)+k \cdot \left(\frac{1}{2} \cdot ((OB)+(OC))-(OA) \right)

    (OG)=(OB)+t \cdot \left(\frac{1}{2} \cdot ((OA)+(OC))-(OB) \right)

    (OG)=(OC)+s \cdot \left(\frac{1}{2} \cdot ((OB)+(OA))-(OC) \right)

    Expand the RHS of this equations. You'll get a system of three linear equations. Solve for k, t, s. You'll get k = t = s = 2/3.

    If you plug in this value into one of the equations above and you'll get your proof.

    Hope that this is of some help.

    Greetings

    EB
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