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Math Help - vectors in regular hexagon

  1. #1
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    vectors in regular hexagon

    a regular hexagon OPQRST has its vertices at O ( the origin) and points P,Q,R, S,T with position vector p,q,r,s,t respectively. The point U with position vector u is the midpoint of the line segment OP, and SU meets OR at the point V
    please see attached diagram


    I need to show that the position vector r=2(p+t) and write down the position vector u and s, in terms of p and t.
    Attached Thumbnails Attached Thumbnails vectors in regular hexagon-hexagone.bmp  
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  2. #2
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    Re: vectors in regular hexagon

    vectors in regular hexagon-hex-sol.png

    Okay. so we need to show r=2(p+t)
    Refer to the figure rohan.
    TOX is congruent to RXQ
    So that OX = XR
    or OR=2*OX -(1)
    now, as SP||OT, PX||OT and also TX||OP
    so that OPXT is a parallelogram
    Now invoking Parallel Law of vector addition, we can say
    OP+OT= OX
    but from (1)
    OP+OT=OR/2
    OR=2(OP+OT)
    r=2(p+t)
    QED

    Hope it helps.
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  3. #3
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    Re: vectors in regular hexagon

    many tnaks- that makes sense.
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  4. #4
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    Re: vectors in regular hexagon

    This is great help- even though you tilted the figure I was able to make sense. further to this I have to now right vector s in terms of t. Can u please look at my original diagram and help thanks
    Thanks from mays
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