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\noindent
\textbf{Directions:}  
\begin{enumerate}
	\item Section: Math251 007
	\item Write your name with one character in each box below.
	\item Show all work.  No credit for answers without work.
\end{enumerate}

\newpage
\headers{Math251-104}{Quiz 4}{Sep 19, 2025}

~
\vspace{1.5cm}

\begin{enumerate}

\newcommand{\myspc}{\vspace{2cm}\\~}

\item\points{3} Give parametric equations for the line through $(2,1,-5)$ that is parallel to $\vect{1,5,-1}$.
\vspace{2cm}

\item\points{3} Give a vector equation for the line at the intersection of planes $x+2y-5z = 5$ and $3x-2y+z=-1$.  
\vspace{4cm}


\item Let $S$ be the plane $2x - y + z = 1$ and let $P$ be the point $(4,2,1)$.
\begin{enumerate}
	\item\points{3} Find the distance between $S$ and $P$.
	\vfill
	\item\points{1} Find the point on $S$ that is closest to $P$.
	\vfill
\end{enumerate}

\end{enumerate}
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