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The Humongous Book of Trigonometry Problems by W. Michael Kelley

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Unit Vectors

Vectors with a magnitude of 1

14.37 Describe the relationship between a vector v and its unit vector .

Given a vector v, the corresponding unit vector has the same direction as v with a magnitude of 1.

Just like a unit circle has a radius of 1, a unit vector has a length of 1.

Note: In Problems 14.38–14.39, v = <4, 3>.

14.38 Given v = <4,3>, express its unit vector in component form.

Begin by calculating the magnitude of v.

To compute ...

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