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 - 14.2 Calculus of Vector-Valued Functions - Exercises - Page 720: 32


$$ L(t)= \langle-16,-20,-36 \rangle +t \langle4,5,9 \rangle .$$

Work Step by Step

Since $ r (t)=\langle4t,5t,9t \rangle, $ then we have the derivative vector $ r' (t)=\langle4,5,9 \rangle $ Then, the parametrization of the tangent line at $ t=-4$ is given by $$ L(t)=r (-4)+tr'(-4)=\langle-16,-20,-36 \rangle +t \langle4,5,9 \rangle .$$
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