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 - 14.1 Vector-Valued Functions - Preliminary Questions - Page 709: 1


(c) $r_3(t) = \langle 8-4t^3, 2+5t^2, 9t^3 \rangle$

Work Step by Step

$r_3(t)$ does not parametrize a line because the components do not have the same degree (the y-component has the the parameter $t$ raised to the second power while the x- and z- components have the parameter $t$ raised to the third power). The equations in (a) and (b) have the parameter $t$ raised to the first and third powers, respectively, in all three components.
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