University Calculus: Early Transcendentals (3rd Edition)

Published by Pearson
ISBN 10: 0321999584
ISBN 13: 978-0-32199-958-0

Chapter 13 - Section 13.6 - Tangent Planes and Differentials - Exercises - Page 727: 2


a) $3x+5y+4z=18$ b) $x=3+6t,y=5+10t; z=-4+8t$

Work Step by Step

a) Since, we have the vector equation $r(x,y,z)=r_0+t \nabla f(r_0)$ The equation of the tangent line is: $\nabla f(3,5,-4)=\lt 6,10,8 \gt$ Thus, $6(x-3)+10(y-5)+8(z+4)=0$ or, $6x+10y+8z=6 \implies 3x+5y+4z=18$ b) Since, we have the vector equation $r=r_0+t \nabla f(r_0)$ Now, the parametric equations are: $\nabla f(3,5,-4)=\lt 6,10,8 \gt$ $x=3+6t,y=5+10t; z=-4+8t$
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