University Calculus: Early Transcendentals (3rd Edition)

Published by Pearson
ISBN 10: 0321999584
ISBN 13: 978-0-32199-958-0

Chapter 12 - Section 12.1 - Curves in Space and Their Tangents - Exercises - Page 649: 27


$|r|$ is constant.

Work Step by Step

Since, $r \dfrac{dr}{dt}=0$ or, $2r \dfrac{dr}{dt}=0$ or, $r \dfrac{dr}{dt}+r \dfrac{dr}{dt}=0$ This implies $\dfrac{d(r\cdot r)}{dt}=0$ or, $\dfrac{d(|r^2|)}{dt}=0$ This means that $|r^2|$ is constant , so $|r|$ is also constant.
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