  We study the vortex state of a layered superconductor with vertical line
nodes on its Fermi surface when a magnetic field is applied in the ab-plane
direction. We rotate the magnetic field within the plane, and analyze the
change of low-energy excitation spectrum. Our analysis is based on the
microscopic
  Bogoliubov-de Gennes equation and a convenient approximate analytical method
developped by Pesch and Dahm. Both methods give a consistent result. Near the
upper critical field H$_{c2}$, we observe a larger zero-energy density of
states(ZEDOS) when the magnetic field is applied in the nodal direction, while
much below H$_{c2}$, larger ZEDOS is observed under a field in the anti-nodal
direction. We give a natural interpretation to this crossover behavior in terms
of momentum distribution of low-energy quasiparticles. We examine the recent
field angle variation experiments of thermal conductivity and specific heat.
Comparison with our results suggest that special care should be taken to derive
the position of line nodes from the experimental data. Combining the
experimental data of the specific heat and our analyses, we conclude that
Sr$_2$RuO$_4$ has vertical line nodes in the direction of the a-axis and the
b-axis.
