University Calculus: Early Transcendentals (3rd Edition)

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

Chapter 11 - Practice Exercises - Page 638: 43


$x=-5+5t; y=3-t; z=-3t$

Work Step by Step

Since, we have $x+2y=1$ and $x-y=-8$ After solving, we get $y=3$ and $x=-8+y=-8+3=5$ The normal to the plane is: $n=\lt 5,-1,-3 \gt$ 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 the point $(-5,3,0 )$, we have the parametric equations: $x=-5+5t; y=3-t; z=0-3t=-3t$ Hence, $x=-5+5t; y=3-t; z=-3t$
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