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 871: 33

Answer

$5x-3y-8z=-9$

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: $25(x-2)-15(y-1)-40(z-2)=0$ $5(x-2)-3(y-1)-8(z-2)=0$ After simplification, we get $5x-3y-8z+9=0$ Or, $5x-3y-8z=-9$
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