Thomas' Calculus 13th Edition

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

Chapter 12: Vectors and the Geometry of Space - Section 12.5 - Lines and Planes in Space - Exercises 12.5 - Page 727: 24



Work Step by Step

The standard equation of plane passing through the point $(a,b,c)$ is given as $p(x-a)+q(y-b)+r(z-c)=0$ Here, the equation of normal to the plane is $n=\lt -1,-3,1 \gt$ For point $(2,4,5)$, we have $(-1)(x-2)+(-3)(y-4)+(1)(z-5)=0$ or, $-x-3y+z=-9$ Thus, $x+3y-z=9$
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