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Calculus II Project Title
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. ||w||²
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. ||w||² = 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.

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