Question

Find the position vector of a point R which divides the line joining two points P and Q whose position vectors are (2a+b) and (a-3b) externally in the ratio 1: 2. Also, show that P is the mid point of the line segment RQ.

Answer 1

It is given that 

It is given that point R divides a line segment joining two points P and Q externally in the ratio 1: 2. Then, on using the section formula, we get:

Hence, P is the mid-point of the line segment RQ.