# Thread: vectors in regular hexagon

1. ## 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

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.

2. ## Re: vectors in regular hexagon

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.

3. ## Re: vectors in regular hexagon

many tnaks- that makes sense.

4. ## 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

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# find the position vector of S in the hexagon opqrst

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