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Q. 1

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Calculus

Found in: Page 879

Book edition 1st

Author(s) Peter Kohn, Laura Taalman

Pages 1155 pages

ISBN 9781429241861

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Short Answer

Unit vectors: If v is a nonzero vector, explain why $\frac{v}{| |v| |}$ is a unit vector.

By definition of a unit vector if v is a nonzero vector then $\frac{v}{||v||}$ is a unit vector.

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1. Given Information.

It is given that v is a non-zero vector.

Step 2. Explanation.

A unit vector is defined as the vector that has a magnitude equal to $1$ and its formula is $\vec{u} = \frac{v}{||v||} .$

If v is a non-zero vector and we divide it by its magnitude, then by the definition of a unit vector it is also a unit vector.

Thus, $\frac{v}{||v||} = \vec{u} .$

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