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: 38


$$r(t)=\lt 2+\cos t,-1+\sin t,4\gt.$$

Work Step by Step

We know that the unit sphere centered at $(2,-1,4)$ has the equation $$(x-2)^2+(y+1)^2+(z-4)^2=1.$$ Its horizontal projection on the xy-plane is $$(x-2)^2+(y+1)^2 =1.$$ So we get the parametrization $$x=2+\cos t, \quad y=-1+\sin t, \quad z=4.$$ That is $$r(t)=\lt 2+\cos t,-1+\sin t,4\gt.$$
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