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Sample Problem and Solution
A sample dot product problem for you to try.
Given u = <2, 2>, v = <5,8>, and w = <4,3>, find each of the following.
a. u v
b. (u v)w
c. u (2v)
d. w²

Solution
a. u v = <2, 2> <5, 8> = 2(5) + (2)(8) = 6
b. (u v)w = 6<4, 3> = <24, 18>
c. u (2v) = 2(u v) = 2(6) = 12
d. w² = w w = <4, 3> <4, 3> = (4)(4) + (3)(3) = 25
You'll probably notice that the answer to part (b) is a vector quantity, while the three other parts yield scalar answers.

Where to from here?
