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~
\vspace{2cm}

\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}{Quiz 2}{Sep 5, 2025}

~
\vspace{1.5cm}

\begin{enumerate}

\newcommand{\myspc}{\vspace{2cm}\\~}
\item\points{3} Find the unit vector in the same direction as $2\mb{i} -3\mb{j} + 6\mb{k}$.  Simplify as much as possible.
\vfill

\item\points{3} Find the vector with magnitude $6$ in the same direction as $\overrightarrow{PQ}$, where $P=(5,2,-1)$ and $Q=(1,2,1)$.
\vfill

\item\points{2} Find a simplified equation in variables $x$, $y$, and $z$ whose solution set equals the points $(x,y,z)$ that are equally distant from $(1,-1,3)$ and $(0,0,0)$.
\vfill

\item\points{2} Vectors $\mb{a}$, $\mb{b}$, and $\mb{c}$ are shown below.  Find a formula for $\mb{c}$ in terms of $\mb{a}$ and $\mb{b}$.
\begin{center}
\begin{tikzpicture}[scale=0.5]
	\draw[->] (0,0) -- (5, 0) node[anchor=west] {$x$} ;
	\draw[->] (0,0) -- (0, 5) node[anchor=east] {$y$} ;
	
	\begin{scope}[every node/.style={circle,fill=black!50,minimum size=0.1ex,inner sep=2pt}]
		\node at (1,1) (A) {} ;
		\node at (2,4) (B) {} ;
		\node at (4,2) (C) {} ;
	\end{scope}
	\begin{scope}[line width=1pt]
	\draw[->] (A) -- node[above,anchor=south east] {$\mb{a}$} (B) ;
	\draw[<-] (B) -- node[above] {$\mb{b}$} (C) ;
	\draw[->] (C) -- node[below] {$\mb{c}$} (A) ;
	\end{scope}
\end{tikzpicture}
\end{center}
\vspace{1cm}

\end{enumerate}
\end{document}
