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The Humongous Book of Trigonometry Problems by W. Michael Kelley

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Dot Product

Looks like multiplication, but it’s not

16.1    Given v = <a, b> and w = <c, d>, explain how to calculate the dot product v · w.

To calculate the dot product of two vectors, add the product of their x-components to the product of their y-components.

v · w = ac + bd

Even though the dot here looks like multiplication, it stands for the “dot product.”

Note: In Problems 16.2–16.4, v = <1, 4> and w = <5, 2>.

16.2    Calculate v · w.

Apply the formula presented in Problem 16.1, which adds the products of the x-components and the y-components.

Note: In Problems 16.2–16.4, v = <1, 4> and w = <5, 2>.

16.3    Calculate 3v · w.

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