Calculus: Early Transcendentals 8th Edition

Published by Cengage Learning
ISBN 10: 1285741552
ISBN 13: 978-1-28574-155-0

Chapter 16 - Section 16.6 - Parametric Surfaces and Their Areas - 16.6 Exercise - Page 1121: 33

Answer

$$3x-y+3z=3$$

Work Step by Step

The normal vector tangent to the plane is: $n=-6u i+2j-6u k$ and the point $(2,3,0)$ corresponds to the parameter values: $n=-6 i+2j-6 k$ When $a$ is the position vector of a point on the plane and $n$ is the vector normal to the plane, then the equation of the plane can be written as: $(r-a) \cdot n=0$ $$ (x-2) \cdot (-6)+(y-3) \cdot (2) +(z-0) \cdot (-6)=0 \\ -6x+12+2y-6-6z=0\\ 3x-y+3z=3$$
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