<html><head><meta name="color-scheme" content="light dark"></head><body><pre style="word-wrap: break-word; white-space: pre-wrap;">\documentclass[a4paper,12pt]{article}
\usepackage{epsfig}
\newcommand{\un}{\underline}
\begin{document}
\parindent=0pt


\begin{center}
\textbf{Vector Fields}

\textit{\textbf{Scalar and Vector Fields}}
\end{center}

\textbf{Question}

Sketch the following plane vector field and determine its field
lines.

$\un{F}(x,y) = \nabla (x^2-y)$


\textbf{Answer}

$\begin{array}{l}
\textrm{The field lines satisfy }\frac{dx}{2x} = \frac{dy}{-1}.\\
\textrm{They are the curves }\\
y=-\frac{1}{2}\ln x+C.
\end{array}
\ \ \ \ \
\begin{array}{c}
\epsfig{file=VF-1A-6.eps, width=40mm}
\end{array}$


\end{document}

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