Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 13 - Vector Functions - Review - True-False Quiz: 12

Answer

True

Work Step by Step

Given; $|r(t)|=1$ for all the value of $t$ $|r(t)|$ can be written as; $|r(t)|=r(t).r(t)$ Thus, $r(t).r(t)=1$ Let us find the derivative. $0=|r(t)|=r'(t).r(t)+r(t).r'(t)$ $2r'(t).r(t)=0$ This implies that $r'(t).r(t)=0$ Therefore, $r'(t)$ is orthogonal to $r(t)$ for any value of $t$. Hence, the given statement is true.
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