Find the position vector of a point R which divides the line joining two points P and Q whose position vectors are

$$(2\overrightarrow{a} + \overrightarrow{b} ) and (\overrightarrow{a} – 3\overrightarrow{b} )$$

externally in the ratio 1 : 2. Also, show that P is the mid point of the line segment RQ.