\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.

$\un{F}(x,y) = y\un{i} +x\un{j}$


\textbf{Answer}

$\begin{array}{l}
\textrm{The field lines satisfy }\frac{dx}{y} = \frac{dy}{x}\\
\rm{Thus\ } xdx=ydy.\\
\textrm{The field lines are the rectangular}\\
\textrm{hyperbola (and their asymptotes)}\\
\textrm{given by }x^2-y^2=C.
\end{array}
\ \ \ \ \
\begin{array}{c}
\epsfig{file=VF-1A-3.eps, width=40mm}
\end{array}$

\end{document}


























