Solutions to this question by accurate drawing will not be accepted.
Relative to an origin \(O\), the position vectors of the points \(A\), \(B\) and \(C\) are \(\overrightarrow{OA}=\begin{pmatrix}1\\7\end{pmatrix}\), \(\overrightarrow{OB}=\begin{pmatrix}7\\4\end{pmatrix}\) and \(\overrightarrow{OC}=k\begin{pmatrix}1\\2\end{pmatrix}\), where \(k\) is a scalar constant.
Given that \(C\) lies on the line \(AB\), use a vector method to find the ratio \(AC:AB\).[6]
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