Calculus (3rd Edition)

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

Chapter 17 - Line and Surface Integrals - 17.1 Vector Fields - Exercises - Page 919: 16

Answer

The planar vector fields satisfies by the $\bf{Plot (A)}$.

Work Step by Step

When we draw a vector field , we need to draw $F(P)$ as a vector based at a point (let us say a point) $P$. The domain of $F$ corresponds to the set of points $P$ for which $F(P)$ is defined. This follows that $F(x,y)=\lt x+y, x-y \gt \quad \text{and} \quad F=(x+y) \ i+(x-y) \ j$ Thus, when we draw a vector field of $F$ at any point the vector will be directed to $(x+y) \ i+(x-y) \ j$ direction. For each point $(a,b)$, we have: $-2 \leq a\leq 2, -2 \leq b \leq 2$ So, we interpret from the above discussion that the planar vector fields satisfies by the $\bf{Plot (A)}$.
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