\documentclass[addpoints,12pt]{exam} % can add 'answers' option
\setlength{\parindent}{0mm}
\usepackage{amsmath}
\usepackage{enumerate}
\usepackage{microtype}
\usepackage{tikz}

\newcommand{\blankunderline}[2]{\makebox[#1]{#2\enspace\hrulefill}}

\newcommand{\dueday}{Sunday}
\newcommand{\duewhen}{1/31/21 at 11:59pm}
\newcommand{\hwnum}{3}
\newcommand{\classnumber}{Math 20C -- Swanson }
\newcommand{\classiteration}{Winter 2021}

\pagestyle{headandfoot}
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\firstpageheader{\classnumber -- \classiteration}{}{Homework \hwnum}
\runningheader{\classnumber}
{Homework, Page \thepage\ of \numpages}
{Due \duewhen}
\firstpagefooter{}{}{}
\runningfooter{}{}{}

\begin{document}
\ 

\begin{center}
  \fbox{\parbox{3in}{\centering\large
  \classnumber -- \classiteration \\
  Homework \hwnum \\
  Due \dueday, \duewhen}}
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\vspace{1cm}
%\blankunderline{0.8\textwidth}{Name:}
%\blankunderline{0.15\textwidth}{Section:}

\vspace{1cm}
\begin{itemize}
  \item The graded part of the homework is on WebAssign.
  \item The problems below are also assigned and you are responsible for doing them,
    but they will not be collected or graded.
\end{itemize}

\newpage

\begin{questions}
  \question Two particles are traveling according to the following parametric equations
  for their position as a function of time:
    \[ \vec{r}_1(t) = \langle 7, 11, -9\rangle + t \langle 2, 3, -1\rangle
          \qquad\text{and}\qquad
        \vec{r}_2(t) = \langle 7, -11, -15\rangle + t\langle -1, 4, 2\rangle. \]
    \begin{enumerate}[(a)]
      \item Determine if the lines on which the two particles are traveling intersect.
        If so, determine all points of intersection.
      \item Determine if the particles collide. If so, determine the time of collision.
    \end{enumerate}
    
    \begin{solution}
      
    \end{solution}
    \newpage
  
  \question
    \begin{enumerate}[(a)]
      \item Suppose that $\vec{a}$ and $\vec{b}$ are nonzero and parallel. Show
        that $\vec{a} \times \vec{b} = \vec{0}$.
      \item Suppose that $\vec{a}$ and $\vec{b}$ are nonzero and
        $\vec{a} \times \vec{b} = \vec{0}$. Show that $\vec{a}$ and
        $\vec{b}$ are parallel.
      \item If $\vec{a} = \vec{0}$ or $\vec{b} = \vec{0}$, what is
        $\vec{a} \times \vec{b}$?
    \end{enumerate}
  
    \begin{solution}
      
    \end{solution}
    \newpage
\end{questions}
\end{document}