\input epsf
\nopagenumbers
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\noindent {\bf Problem statement} Suppose the line $L_1$ is
$\cases{x=2t+1\cr y=-t-1\cr z=3t\cr}$ and the line $L_2$ is
$\cases{x=3s+2\cr y=5s-2\cr z=-4\cr}$. Define the function $f(s,t)$ to
be the distance between the point on line $L_1$ with parameter value
$s$ and the point on the line $L_2$ with parameter value $t$.

\medskip

\noindent a) Find and classify (max/min/saddle) all critical points of
$f(s,t)$. (There is exactly one!)

\medskip

\noindent b) The line segment which has endpoints characterized by the
values of $s$ and $t$ discovered in a) has an interesting geometric
property related to $L_1$ and $L_2$. What is this property? Use a
drawing to help your explanation.

\vfil\eject\end