The process e gamma -> eZ/gamma* is studied in e+e- collisions with the OPAL detector at LEP at a centre-of-mass energy of sqrt(s) = 189 GeV. The e+e- cross-section times the branching ratio of the Z/gamma* decaying into hadrons is measured within Lorentz invariant kinematic limits. The differential e+e- cross-sections of the Mandelstam variables s, t, and u are measured and compared with the predictions from the Monte Carlo generators grc4f and PYTHIA. The e gamma cross-section times the branching ratio of the Z/gamma* decaying into hadrons is measured as a function of the centre-of-mass energy of the e gamma system. The differential e gamma cross-sections dsigma/dt and dsigma/du are also measured.