restart:
with(VectorCalculus):
#
# Define a position vector in spherical polars, hold the second
# entry at Pi/2 and vary the third entry. If the second entry
# is the zenith angle then this should produce only vectors in
# the x-y plane
#
# In other words the *third* entry in every output vector should
# be zero - which it is
#
seq( PositionVector([1, Pi/2, j*Pi/4], spherical), j=0..8);
#
# Define a position vector in spherical polars, hold the third
# entry at 0 and vary the second entry. If the second entry
# is the zenith angle then this should produce only vectors in
# the x-z plane
#
# In other words the *second* entry in every output vector should
# be zero - which it is
#
seq( PositionVector([1, j*Pi/4, 0], spherical), j=0..4);#
# Define a position vector in spherical polars, hold the third
# entry at Pi/2 and vary the second entry. If the second entry
# is the zenith angle then this should produce only vectors in
# the y-z plane
#
# In other words the *third* entry in every output vector should
# be zero - which it is
#
seq( PositionVector([1, j*Pi/4, Pi/2], spherical), j=0..4);#
# The above seems to confirm that if a triple [u, v, w] is
# defined to be in spherical coordinates, the second entry is
# the zenith angle and the third is the azimuth. This seems to
# confirm that the definition page in the Maple help is correct
# but the coords help page is wrong