\documentclass[12pt]{article}

\usepackage{amssymb,amsmath,amsthm,amsfonts,amscd,latexsym, dsfont, color, xcolor}
\usepackage{hyperref} 

\hypersetup{colorlinks}
\usepackage{graphicx}

\newcommand{\R}{\mathbb R}
\newcommand{\C}{\mathbb C}
\newcommand{\Z}{\mathbb Z}
\newcommand{\Q}{\mathbb Q}
\newcommand{\op}[1]{\operatorname{#1}}
\usepackage[margin=.75in]{geometry}
%\setlength{\topmargin}{0in}
\setlength{\textheight}{9in}
\begin{document}
\pagestyle{empty}

{\bf Math 222 in class problems} \hspace{.5in} \textbf{Week: February 8, 2021} %outlier malcom
\begin{enumerate}


%\item Multi Warm Up \\
%Reparametrize the below curve by arc length from $(1,1,0)$ in the direction of increasing $t$
%\[
%r(t)= \langle e^t,  e^{-t}, t\sqrt{2}   \rangle.
%\]
%Then compute $\mathbf{T}, \mathbf{N}, \mathbf{B}$, $k(s)$, and $\tau(s)$.

\item Problem 8-1: Jones \\
Consider the ``parallelogram" in $\R^3$ with ``edges" equal to the three points $\mathbf{i}, \mathbf{j}, \mathbf{i}-2\mathbf{j}$.  Draw a sketch of it and conclude that it is actually a six-sided figure in the $xy$-plane.



 
\item Problem 8-2: Jones  \\
Compute the area of the triangle in $\R^3$ whose vertices are $a\mathbf{i}, \ b\mathbf{j}, \  c\mathbf{k}$.  \\ Optional: Express the result in a form that is a symmetric function of $a,b,c$.



\end{enumerate}
 
Hint for \#2:

\begin{figure}[h]
\begin{centering}
  \includegraphics[width=.9\linewidth]{jones_example_8.png}
  \caption{Example on Jones 8-4}
  \label{fig:boat1}
\end{centering}
\end{figure}

\vfill
\eject



\end{document}




