Vector

Geometry Level 3

The coordinates of \(A, B\) and \(C\) are \((1,2), (7,1)\) and \((15,9)\), respectively. \(O\) is the origin and \(\overrightarrow{OC}\,=\,h\overrightarrow{OA}\,+\,k\overrightarrow{OB}\), where \(h\) and \(k\) are constants. If \(h+k\) can be expressed as \(\dfrac{m}{n}\), where \(m\) and \(n\) are coprime positive integers, find \(m+n\).

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