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Basic vectors Q

  1. Oct 25, 2013 #1
    htyNwwS.png

    I can't even get started on part i), if anyone could give me a starting point and see where I go from there... thanks
     
  2. jcsd
  3. Oct 25, 2013 #2

    FeDeX_LaTeX

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    Gold Member

    I would start by drawing a picture. In part (i), they are asking for a proof of a very popular theorem in geometry; that each of the medians (the lines drawn from each vertex to the mid-point of the opposite side) intersect such that the median is split into two segments in the ratio 2:1 (i.e. the intersection is two thirds of the length of the median away from the vertex). Can you prove this?
     
  4. Oct 25, 2013 #3

    berkeman

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    Staff: Mentor

    To get started, draw the figure and label all the points and vectors...
     
  5. Oct 25, 2013 #4
    no I can't construct a proof of this using vectors, i've constructed it using a coordinate system before but not with vectors. Using this fact I was able to prove i), but I'm not sure how I can prove the fact (which I'm sure I'll have to do)

    I've done this, thanks.
     
  6. Oct 26, 2013 #5
    here is what I have for part i):

    ## \vec{OL} = \dfrac{1}{2}(\vec{OA} + \vec{OC}) ##
    ## \vec{OG} = \vec{OB} + \dfrac{2}{3} \vec{BL} ##
    ## \vec{BL} = \vec{OL} - \vec{OB} = \dfrac{1}{2} (\vec{OA} + \vec{OC}) - \vec{OB} ##
    subbing this into ## \vec{OG} ## I get the required result

    I think I need to prove that the medians are split in a 2:1 ratio, but how would I do it using vectors?

    Also for part ii)what do they mean by ## a^2 + b^2 + c^2 ## it makes a note that ## a = |\vec{BC}| ## then what is b and c?
     
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