  We consider a singly quantized off-axis straight vortex in a rotating dipolar
ultracold gas in the Thomas-Fermi (TF) regime. We derive analytic results for
small displacements and perform numerical calculations for large displacement
within the TF regime. We show that the dipolar interaction energy increases
(decreases) as the vortex moves from the trap center to the edge in an oblate
(a prolate) trap. We find that for an oblate (a prolate) trap, the effect of
the dipole-dipole interaction is to lower (raise) both the precession velocity
of an off-center straight vortex line and the angular velocity representing the
onset of metastability.
