Question

Prove that position vector of the centroid of a triangle ABC is 1/3 vector ( a + b + c ), where, vector (a , b & c) are the position vectors of the vertices A , B & C w.r.t. some fixed point O.

Answer 1

Let O be the fixed point

let AD be the median of the triangle ABC 

Since D is the mip point of BC

Position vector of D = vector (OD = (OB + OC)) / 2 

Since , G divides internally AD in the ratio 2 : 1