A good answer might be:

c is much longer vector than b; it is likely that a · c is the larger.

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.


What is the normal method for removing the influence of length?