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Paradigm$\newline$Specialising in O Level Mathematic$\newline$In the diagram, $A B C$ is a triangle where $M$ is the midpoint of $A C$.$\newline$The point $P$ lies on the line $B M$ such that $B P=\frac{1}{3} B M$.$\newline$The point $Q$ lies on the line $B C$ such that $B Q: Q C=1: 4$.$\newline$Given that $\overrightarrow{A B}=b$ and $M$$0$.$\newline$(a) Express, as simply as possible, in terms of $M$$1$ and or $M$$2$,$\newline$(i) $M$$3$,