<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}
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\begin{center}
\textbf{Vector Fields}

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

\textbf{Question}

Describe the streamlines of the following velocity field.

$\un{v}(x,y,z) = e^{xyz}(x \un{i} +y^2 \un{j} + z\un{k})$


\textbf{Answer}

The field lines satisfy $\frac{dx}{x}=\frac{dy}{y^2}=\frac{dz}{z}$.

So they are given by $z=C_1x$, $\ln |x| = \ln |C_2|-(1/y) $ (or,
equivalently, $x=C_2e^{-1/y}$.)

\end{document}

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