University Calculus: Early Transcendentals (3rd Edition)

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

Chapter 11 - Section 11.5 - Lines and Planes in Space - Exercises - Page 631: 31

Answer

$x-y+z=0$

Work Step by Step

The normal to the plane is $n=\lt 3,-3,3 \gt$ We know that the standard equation of a plane passing through the point $(x_0,y_0,z_0)$ is written as: $a(x-x_0)+b(y-y_0)+c(z-z_0)=0$ Then for point $(2,1,-1)$, we have $3(x-2)-3(y-1)+3(z+1)=0$ or, $3x-3y+3z=0$ or, $x-y+z=0$
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