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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.

$\un{v}(x,y,z) = xz\un{i} +yz\un{j} +x\un{k}$


\textbf{Answer}

The field lines satisfy $\frac{dx}{xz}=\frac{dy}{y^2}=\frac{dz}{x}$,
or equivalently, $\frac{dx}{x}=\frac{dy}{y}$ and $dx=zdz$.

Thus the field lines have equations $y=C_1x$, $2x=z^2+C_2$
and are therefore parabolas.

\end{document}