Efficient distance calculation between N points and a reference in numpy/scipy

I would take a look at scipy.spatial.distance.cdist:

http://docs.scipy.org/doc/scipy/reference/generated/scipy.spatial.distance.cdist.html

import numpy as np
import scipy

a = np.random.normal(size=(10,3))
b = np.random.normal(size=(1,3))

dist = scipy.spatial.distance.cdist(a,b) # pick the appropriate distance metric 

dist for the default distant metric is equivalent to:

np.sqrt(np.sum((a-b)**2,axis=1))  

although cdist is much more efficient for large arrays (on my machine for your size problem, cdist is faster by a factor of ~35x).