Calculus, 10th Edition (Anton)

Published by Wiley
ISBN 10: 0-47064-772-8
ISBN 13: 978-0-47064-772-1

Chapter 15 - Topics In Vector Calculus - 15.1 Vector Fields - Exercises Set 15.1 - Page 1092: 6

Answer

The vector field $\mathbf{F}(x,y)=y\,\mathbf{j}$ consists of upward-pointing\\ vectors whose magnitude increases as $y$ increases.\\ There is no field defined below the $x$-axis $(y<0)$. };

Work Step by Step

Explanation: The field $\mathbf{F}(x, y) = y\,\mathbf{j}$ has vectors pointing straight upward because it has only a $j$-component. The magnitude of each vector is proportional to $y$, so as we move upward, the arrows become longer. For $y > 0$, the field is nonzero; below the $x$-axis ($y < 0$), the field is undefined or absent.
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