In a triangle, the position vectors of the vertices with respect to the origin are a,b and c.
a. (i) Show that the midpoint of the side BC has position vector 2b+c.
b. (ii) Obtain the vector equation of the median drawn from vertex A.
c. (iii) Prove that the three medians of the triangle are concurrent and that the position vector of their point of intersection is 3a+b+c.