Thomas' Calculus 13th Edition

Published by Pearson
ISBN 10: 0-32187-896-5
ISBN 13: 978-0-32187-896-0

Chapter 12: Vectors and the Geometry of Space - Questions to Guide Your Review - Page 733: 1


Explanation given below.

Work Step by Step

Two vectors are equal if they have the same direction and have the same magnitude (length). So, two directed line segments $\overrightarrow{AB}$ and $\overrightarrow{CD} $ represent the same vector if 1. The directions (unit vectors), $\displaystyle \frac{\overrightarrow{AB}}{|\overrightarrow{AB}|} $ and $\displaystyle \frac{\overrightarrow{CD}}{|\overrightarrow{CD}|}$ are equal and 2. $|\overrightarrow{AB}|$=$|\overrightarrow{CD}|\qquad $; that is, they have equal magnitudes (lengths)
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