% TEMPLATE FOR STANDARD QUIZ
% by laura
\documentclass[14pt,epsfig]{article}

\usepackage{graphicx}
\usepackage{amsmath}
\usepackage{amssymb}
\oddsidemargin=0in
\evensidemargin=0in
\textwidth=6.3in
\topmargin=-0.5in
\textheight=9in

\parindent=0in
\pagestyle{empty}

%%%begin testpoints.tex
\oddsidemargin=0in
\evensidemargin=0in
\textwidth=6.3in
\topmargin=-0.5in
\textheight=9in
\parindent=0in
\pagestyle{empty}

\newcounter{problemnum}
\renewcommand{\theproblemnum}{\arabic{problemnum}}
\newcounter{partnum}[problemnum]
\renewcommand{\thepartnum}{\alph{partnum}}
\newcounter{totalpoints}
\newcounter{curprobpts}	
\newcounter{totalparts}
\newcounter{pagepoints}
\newenvironment{problem}[1]{
\refstepcounter{problemnum}
\vspace{0.15in} \par
\setcounter{curprobpts}{#1} \setcounter{totalparts}{0}
{\Large \bf \theproblemnum. \normalsize ({\it \arabic{curprobpts} point\null\ifnum \value{curprobpts} = 1\else s\fi}\/)}
}{\ifnum \value{totalparts} = 0
	\addtocounter{totalpoints}{\value{curprobpts}}	% Add pts to total.
	\addtocounter{pagepoints}{\value{curprobpts}}
	\else \ifnum \value{totalparts} = \value{curprobpts}
	\else \typeout{}
	\typeout{!!!!!!!   POINT ACCOUNTING ERROR   !!!!!!!!}
	\typeout{PROBLEM [\theproblemnum] WAS ALLOCATED \arabic{curprobpts} POINTS,}
	\typeout{BUT CONTAINS PARTS TOTALLING \arabic{totalparts} POINTS!}
	\typeout{}
	\fi
\fi
}
\newcommand{\newpart}[1]
{
\refstepcounter{partnum}
\hspace{0.25in}	
\ifnum #1 > 0
	\makebox[0.5in][l]{{\bf \thepartnum.} {\bf ({\it #1 pt\ifnum #1 = 1\else s\fi\/}) \,\,}}
\else
	\makebox[0.25in][l]{({\bf \thepartnum})}
\fi
\hspace{0.1in}	
\addtocounter{totalparts}{#1}
\addtocounter{pagepoints}{#1}
\addtocounter{totalpoints}{#1}
}
\newcommand{\skipproblem}[1]{\addtocounter{problemnum}{#1}}

\newcommand{\showpoints}
{
\typeout{}  
\typeout{====> A TOTAL OF \arabic{totalpoints} POINTS WERE READ.}
\typeout{}
}
%%%end testpoints.tex
%\input{testpoints}

\begin{document}


%%%(change to appropriate class and semester)
MATH 2222H{\&}J Spring 2016

%%%(change to appropriate quiz type and date)
Quiz 1 \hspace{1.9in} {Name:} {\underline {\hspace{2.5in}}}
\vspace{2pc}

%%%(modify rules, time, points as appropriate)
Show all work clearly and in order, and circle your final answers.  

Justify your answers algebraically whenever possible. Unjustified work may not receive full credit. \\
\vspace{2pc}

\begin{problem}{1}
What does the equation $x^2+(y-1)^2=4$ describe in $\mathbb{R}^2$?
\vfill
\end{problem}
\begin{problem}{2}
Let $\vec{a}=<3,1,2>$ and $\vec{b}=<-1,4,3>$. Calculate $\lVert \vec{a} \rVert$, $\vec{a}-7\vec{b}$, and $\lVert 2\vec{a}-7\vec{b} \rVert$.
\vfill
\end{problem}

\begin{problem}{2}
Let $P=(3,4,-1)$ and $Q=(2,2,1)$ be points in $\mathbb{R}^3$. Find the vectors $\overrightarrow{PQ}$ (the vector from $P$ to $Q$) and $\overrightarrow{QP}$ (the vector from $Q$ to $P$). What relationship does $\overrightarrow{PQ}$ have to $\overrightarrow{QP}$?
\vfill
\end{problem}

\showpoints
\end{document}