Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 12 - Vectors and the Geometry of Space - 12.5 Equations of Lines and Planes - 12.5 Exercises - Page 872: 35

Answer

$8x+y-2z=31$

Work Step by Step

The general form of the equation of the plane passing through the point $(a,b,c)$ and having normal vector $\lt l,m,n\gt$is: $l(x-a)+m(y-b)+n(z-c)=0$ Thus, the equation of plane is: $-16(x-3)-2(y-5)+4(z+1)=0$ After simplification, we get $-16x-2y+4z+62=0$ Or, $8x+y-2z=31$
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