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\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.

$\displaystyle \un{v}(x,y,z) = \frac{x\un{i} +
y\un{j}}{(1+z^2)(x^2+y^2)}$


\textbf{Answer}

The streamlines satisfy $dz=0$ and $\frac{dx}{x} = \frac{dy}{y}$.
Thus $z=C-1$ and $y=C_2x$.

The streamlines are horizontal half-lines emanating from the $z$-axis.


\end{document}

