  We have measured the Zeeman splitting of quantum levels in few-electron
quantum dots (QDs) formed in narrow bandgap InSb nanowires via the Schottky
barriers at the contacts under application of different spatially orientated
magnetic fields. The effective g-factor tensor extracted from the measurements
is strongly anisotropic and level-dependent, which can be attributed to the
presence of strong spin-orbit interaction (SOI) and asymmetric quantum
confinement potentials in the QDs. We have demonstrated a successful
determination of the principal values and the principal axis orientations of
the g-factor tensors in an InSb nanowire QD by the measurements under rotations
of a magnetic field in the three orthogonal planes. We also examine the
magnetic-field evolution of the excitation spectra in an InSb nanowire QD and
extract a SOI strength of $\Delta_{so}\sim 180$ $\mu$eV from an avoided level
crossing between a ground state and its neighboring first excited state in the
QD.
