How can a list of vectors be elegantly normalized, in NumPy?

Here is an example that does not work:

from numpy import *

vectors = array([arange(10), arange(10)])  # All x's, then all y's
norms = apply_along_axis(linalg.norm, 0, vectors)

# Now, what I was expecting would work:
print vectors.T / norms  # vectors.T has 10 elements, as does norms, but this does not work

The last operation yields "shape mismatch: objects cannot be broadcast to a single shape".

How can the normalization of the 2D vectors in vectors be elegantly done, with NumPy?

Edit: Why does the above not work while adding a dimension to norms does work (as per my answer below)?