Thomas' Calculus 13th Edition

Published by Pearson
ISBN 10: 0-32187-896-5
ISBN 13: 978-0-32187-896-0

Chapter 14: Partial Derivatives - Section 14.6 - Tangent Planes and Differentials - Exercises 14.6 - Page 833: 8


$9x-7y-z=21$ b) $x=2+9t,y=-3-7t; z=18-t$

Work Step by Step

The vector equation is given by: $r(x,y,z)=r_0+t \nabla f(r_0)$ The equation of tangent line is given as: $\nabla f(2,-3,18)=\lt 9,-7,-1 \gt$ Now, $(9)(x-2)-(7)(y+3)-(1)(z-18)=0 \implies 9x-7y-z=21$ b. The vector equation is give as: $r=r_0+t \nabla f(r_0)$ we have the parametric equations as follows: $x=2+9t,y=-3-7t; z=18-t$
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