Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 13 - Vector Geometry - 13.5 Planes in 3-Space - Exercises - Page 685: 34

Answer

The plane is parallel to the $z$-axis. The trace is the line $x+2y=6$.

Work Step by Step

To draw the plane, we determine its intersections with the coordinate axes. Since $z$ coordinate is not present in the equation, it does not intersects the $z$-axis. So, the plane is parallel to the $z$-axis. To find where it intersects the $x$-axis, we set $y=0$ and obtain $x=6$. It intersects the $y$-axis when $x=0$. So, $y=3$. Thus, the trace is the line $x+2y=6$. The plane is shown in the figure attached.
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