Prove that the medians of a triangle are concurrent and find the position vector of the point of concurrency (that is, the centroid of the triangle)

Explanation

Let A,B and C be vertices of a triangle.

Let D,E and F be the midpoints of the sides BC,AC and AB respectively. Let OA=a
,OB=b,OC=c,OD=d,OE=e
and OF=f

​ be position vectors of points A,B,C,D,E and F respectively.

Therefore, by Midpoint formula,

`d=(b+c)/2,=(a+c)/2
​` and `f​=(a+b)/2`

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