Given vectors OA = a and OB = b, with X on OA such that OX = 5/4 OA, Y on OB such that OY = 2 OB, and C such that AC = 6 AB, and O, B, C are collinear, find OC.

Let O be the origin. We are given the position vectors $\vec{OA} = \mathbf{a}$ and $\vec{OB} = \mathbf{b}$.

From the problem statement:

1. $\vec{OX} = \frac{5}{4}\vec{OA} = \frac{5}{4}\mathbf{a}$
2. $\vec{OY} = 2\vec{OB} = 2\mathbf{b}$
3. $\vec{AC} = 6\vec{AB}$

From the diagram, points O, B, C are collinear. This means $\vec{OC}$ is a scalar multiple of $\vec{OB}$. Let $\vec{OC} = k\vec