  We study experimentally the line of a single quantized vortex in a rotating
prolate Bose-Einstein condensate confined by a harmonic potential. In agreement
with predictions, we find that the vortex line is in most cases curved at the
ends. We monitor the vortex line leaving the condensate. Its length is measured
as a function of time and temperature. For a low temperature, the survival time
can be as large as 10 seconds. The length of the line and its deviation from
the center of the trap are related to the angular momentum per particle along
the condensate axis.
