Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 14 - Calculus of Vector-Valued Functions - 14.3 Arc Length and Speed - Preliminary Questions - Page 725: 1

Answer

If the speed were doubled, $r'=\langle 50, -70, 20 \rangle$. If the direction were reversed, $r'=\langle -25, 35, -10 \rangle$.

Work Step by Step

When the speed doubles, each component simply gets doubled, so $r'=2*\langle 25, -25, 10 \rangle = \langle 50, -70, 20 \rangle$. When the direction gets reversed, each component simply gets multiplied by -1, so $r'=-1*\langle 25, -25, 10 \rangle = \langle -25, 35, -10 \rangle$.
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