The diagram shows the triangle \(OAB\) with \(\overrightarrow{OA}=\mathbf a\) and \(\overrightarrow{OB}=\mathbf b\). The point \(X\) lies on the line \(OA\) such that \(\overrightarrow{OX}=\frac35\mathbf a\). The point \(Y\) is the midpoint of the line \(AB\). Find, in terms of \(\mathbf a\) and \(\mathbf b\),

(a) \(\overrightarrow{AB}\),

(b) \(\overrightarrow{XY}\).

The lines \(OB\) and \(XY\) are extended to meet at the point \(Z\). It is given that \(\overrightarrow{YZ}=\lambda\overrightarrow{XY}\) and \(\overrightarrow{BZ}=\mu\mathbf b\).

(c) Find \(\overrightarrow{XZ}\) in terms of \(\lambda\), \(\mathbf a\) and \(\mathbf b\).

(d) Find \(\overrightarrow{XZ}\) in terms of \(\mu\), \(\mathbf a\) and \(\mathbf b\).

(e) Hence find the values of \(\lambda\) and \(\mu\).