Find the position vector of a point R which divides the line segment joining points and in the ratio 2 : 1.

(i) Internally

(ii) Externally

By using section formula,

(1) Internally

Position vectors of P and Q are given as

and

The position vector of point R which divides the line joining two points P and Q internally in the ratio 2 : 1 is given by,

The position vector of point R which divides the line joining two points P and Q externally in the ratio 2 : 1 is given by,

(2)Externally