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Answer:

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

Length Affects Dot Product

three vectors, separated by 30 degrees

The answer is not only likely, but correct.

a is (6,  0)T
b is (3,  2)T
c is (5,  9)T

The dot products are:

a · b   is 18.0
a · c   is 30.00

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

QUESTION 3:

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