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 - Exercises - Page 711: 37


$$r(t)=\lt t,3t,15t\gt.$$

Work Step by Step

Since the projection of the line on the xy-plane is a line of slope 3, then $y=3x$ and since its projection on the yz-plane is a line of slope 5, then $z=5y$. Now, let $x=t$; then $y=3t$ and $z=5y=5(3t)=15t$ and we get the parametrization $$r(t)=\lt t,3t,15t\gt.$$ (Where $t$ can be any real number.)
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