we have
![](https://latex.codecogs.com/png.latex?\bg_white \overrightarrow{OD}= \frac{1}{5} (4a+2b) )
So you need to think about the distance from a / b in terms of
![](https://latex.codecogs.com/png.latex?\bg_white \overrightarrow{OD}+\frac{3}{5} \overrightarrow{AB} = b)
So then its closer to A, idk how they got 1/2. I would show more working like
![](https://latex.codecogs.com/png.latex?\bg_white \overrightarrow{OD}+\lambda \overrightarrow{AB}=a, b)
maybe I'm missing something since I didn't do i)
Edit: they got 1/2 since if its less than 1/2 obviously its closer