Length Affects Dot Product

The answer is not only likely, but correct.

a is (6,  0)^T

b is (3,  1.9)^T

c is (5,  9)^T

The dot products are:

a · b   is 15.0

a · c   is 30.00

So there are two properties tangled up in the dot product: the angle between the input vectors, and the length of the input vectors. We would like to get at just the angle alone by somehow removing the influence of length.