Answer:
Let \[\overrightarrow{OA}=\vec{a},\,\,\overrightarrow{OB}=\vec{b}\] and \[\overrightarrow{OC}=\vec{c}\] We have, \[\overrightarrow{BC}=1.5\,\,\overrightarrow{BA}\] \[\because \] \[\overrightarrow{BC}=\overrightarrow{OC}-\overrightarrow{OB}\] and \[\overrightarrow{BA}=\overrightarrow{OA}-\overrightarrow{OB}\] \[\therefore \] \[\overrightarrow{OC}-\overrightarrow{OB}=1.5(\overrightarrow{OA}-\overrightarrow{OB})\] \[\Rightarrow \] \[\overrightarrow{OC}-\vec{b}=1.5(\vec{a}-\vec{b})\] \[\Rightarrow \] \[\overrightarrow{OC}=1.5\vec{a}\,\,-1.5\,\vec{b}+\vec{b}\] \[=1.5\vec{a}\,\,-0.5\,\vec{b}\] \[=\frac{3}{2}\vec{a}\,\,-\frac{1}{2}\,\vec{b}\] \[\Rightarrow \] \[\vec{c}=\frac{3\vec{a}-\vec{b}}{2}\]
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