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: 36


$$r(t)=\lt1+3t, t,4-2t\gt$$ (Other answers are possible.)

Work Step by Step

Since the line passes through $(1,0,4)$ and $(4,1,2)$, then the direction vector is given by $$(4,1,2)-(1,0,4)=\lt3,1,-2\gt$$ and the equation of the line is given by $$r(t)=\lt1+3t,0+t,4-2t\gt=\lt1+3t, t,4-2t\gt$$
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