The position vectors of two points A and B are and respectively. Find the position vector of a point C which divides AB externally in the ratio 1 : 2. Also, show that A is the mid-point of the line segment CB.

Formula to be used – The point dividing a line joining points a and b in a ratio m:n externally is given by respectively.

The position vector of the point C dividing the line externally

The midpoint of B and C may be given by

i.e. point A

A is the midpoint of B and C.