If $\vec{a}$ and $\vec{b}$ are the position vectors of $A$ and $B$,respectively,find the position vector of a point $C$ in $BA$ produced such that $BC = 1.5 BA$.

(N/A) Given that $\overrightarrow{OA} = \vec{a}$ and $\overrightarrow{OB} = \vec{b}$.
We know that $\overrightarrow{BA} = \overrightarrow{OA} - \overrightarrow{OB} = \vec{a} - \vec{b}$.
According to the problem,the point $C$ is on the line $BA$ produced such that $\overrightarrow{BC} = 1.5 \overrightarrow{BA}$.
Therefore,$\overrightarrow{BC} = 1.5(\vec{a} - \vec{b})$.
Since $\overrightarrow{BC} = \overrightarrow{OC} - \overrightarrow{OB}$,we have:
$\overrightarrow{OC} - \overrightarrow{OB} = 1.5\vec{a} - 1.5\vec{b}$.
Substituting $\overrightarrow{OB} = \vec{b}$,we get:
$\overrightarrow{OC} = 1.5\vec{a} - 1.5\vec{b} + \vec{b}$.
$\overrightarrow{OC} = 1.5\vec{a} - 0.5\vec{b}$.
This can be written as $\overrightarrow{OC} = \frac{3\vec{a} - \vec{b}}{2}$.