Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 13 - Vector Geometry - 13.5 Planes in 3-Space - Exercises - Page 684: 24

Answer

$$ y=5.$$

Work Step by Step

Since the plane is parallel to the $ xz $-plane $$ y=0$$ then its normal vector $ n $ is $\langle 0,1,0\rangle $ and, using the fact that the plane passes through $(3,5,-9)$, the equation of the plane is given by $$0(x-3)+(y-5)+0(z+9)=0\Longrightarrow x-5=0$$ Hence the equation is given by $$ y=5.$$
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