Calculus: Early Transcendentals 8th Edition

Published by Cengage Learning
ISBN 10: 1285741552
ISBN 13: 978-1-28574-155-0

Chapter 12 - Section 12.5 - Equations of Lines and Planes - 12.5 Exercises - Page 832: 63

Answer

$\frac{x}{a}+\frac{y}{b}+\frac{z}{c}=1$

Work Step by Step

Normal vector is: $\lt bc,ac,ab\gt$ The general form of the equation of the plane is: $a(x-x_0)+b(y-y_0)+c(z-z_0)=0$ or, $ax+by+cz=ax_0+by_0+cz_0$ Here, $n=\lt bc,ac,ab\gt$ and $r_0=(a,0,0)$ Thus, $bc(x-a)+ac(y-0)+ab(z-0)=0$ $xbc+yac+zab=abc$ Divide throughout by $abc$ and we get $\frac{x}{a}+\frac{y}{b}+\frac{z}{c}=1$
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