Let 
be the position vectors of the vertices of a triangle ABC . Through the vertices, lines are drawn parallel to the sides to form the triangle 
. Then the centroid of 
is
Text Solution
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is vector passing through 
parallel to
similarly
For point of intersection 
, solving pairwise above equations
From (i) & (ii)
Put 
in (i)
Position vector of 
Form (ii) & (iii)
Substituting values of 
in equations.
Position vector of 
Position vector of 
Position vector of centroid of 
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