Using the provided diagram and vector notation, determine the vector OX.

Let's break down this vector geometry problem.

First, we establish the position vectors based on the given information and the diagram.
Let O be the origin $(0,0)$.
From the diagram:
$\vec{OA} = \mathbf{a}$
$\vec{OB} = \mathbf{b}$

From the ratios indicated on the diagram:

• Point A divides OX such that $OA:AX = 4:1$. This means $\vec{OX} = \frac{4+1}{4} \vec{OA} = \frac{5}{4} \vec{OA}$. So, $\vec{OX} = \frac{5}{4} \mathbf{a}$.