Let OPQR be a parallelogram with O as the origin. The position vectors along OP and OR are respectively. S is a point on OP which divides it in the ratio 1: 3. If SR intersects OQ in M whose position vector is then find the value of . please explain i did not understand what does it meant?

Let OQ have position vector as s
Hence OQ  = s = a + b 

As S divides OP in the ratio 1: 3
Hence by section formula
S have position vector as  = [3(0) + 1(a)] / [3+1]  = a/4

Let M divides RS in the ratio of r : 1

Hence the position vector of M = $\frac{r\times {\displaystyle \frac{\mathit{a}}{4}} +\mathit{b}}{r+1}$ (1)
But the position vector of M is given as  = $\mu (\mathit{a} +\mathit{b})$  (2)
When we have r = 4  , then M = 4(a+b) /(4*5) = 1/5 (a+b ) 
Comparing (1) with (2) , we have $\mu = \frac{1}{5}$