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{Mathematical Physics --- PHZ 3113}\\\vspace {2mm} 
Vector Integration Homework\\ (February 20, 2013) \\
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\noindent Integrate (explicitly!) the force
\begin{eqnarray} \label{F}
  \vec{F} = - x_2\,\hat{x}_1 + x_1\,\hat{x}_2
\end{eqnarray} 
in anti-clockwise direction along the boundary of an
equilateral triangle in the $x_1-x_2$ plane. The triangle
has a side from $(0,0)$ to $(a,0)$ on the $x_1$ axis and 
closes in the upper half of the $x_1-x_2$ plane.  \vfil
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