Three particles each of mass m, are placed at the corners of an equilateral triangle of side a, as shown in Fig. The position vector of the centre of mass is

Refer to Fig. The (x, y) co-ordinates of the masses at 0, A and B respectively are x1=0,y1=0,x2=a,y2=0,x3=a2,y3=a32Therefore, the (x, y) co-ordinates of the centre of mass are  xCM=m×0+m×a+m×a/2m+m+m=a2yCM=m×0+m×0+m×a3/2m+m+m=a23∴Position vector of centre of mass is a2i^+j^3.