Multivariable Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 0-53849-787-4
ISBN 13: 978-0-53849-787-9

Chapter 13 - Vector Functions - 13.1 Exercises - Page 870: 30

Answer

$(0.909,-0.416,2)$ and $(-0.909,-0.416,-2)$

Work Step by Step

Write the parametric equations from the given problem $r(t)= (\sin^2 t+\cos^2 t)+t^2=5$ as follows: That is, $\sin^2 t+\cos^2 t=1$ When we plug these parametric equations in to the given paraboloid equation: $z=x^2+y^2 \implies 1+t^2=5$ and $t^2=4; t= \pm 2$ Thus we have the point of intersection $ \lt \sin 2, \cos 2, 2 \gt$ Re-arrange as: $ \lt \sin (-2), \cos (-2), 2 \gt$ Hence, we get $(0.909,-0.416,2)$ and $(-0.909,-0.416,-2)$
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