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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.

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


\textbf{Answer}

The streamlines satisfy  $\frac{dx}{x}=\frac{dy}{y}=\frac{dz}{x}$.
Thus $z+x=C_1$, $y=C_2x$.

The streamlines are straight half-lines emanating from the
$z$-axis and are perpendicular to the vector $\un{i}+\un{k}$.

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