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

Question

$\begin{array}{1 1} (A)\;\Large\frac{3 \overrightarrow{b}- \overrightarrow{a}}{2} \\(B)\;\Large\frac{3 \overrightarrow{a}- \overrightarrow{b}}{2} \\ (C)\;\Large\frac{9 \overrightarrow{a}-4 \overrightarrow{b}}{2} \\ (D)\;\Large\frac{3 \overrightarrow{a}+ \overrightarrow{b}}{2}\end{array} $