Points \(A\) and \(B\) have position vectors \(\mathbf{a}=\begin{pmatrix}5\\-1\end{pmatrix}\) and \(\mathbf{b}=\begin{pmatrix}-1\\7\end{pmatrix}\). Point \(P\) divides \(AB\) internally in the ratio \(AP:PB=4:3\). Find the position vector of \(P\).
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