% Simplified version of an UMTYMP template.
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% If the text is too small, change 10pt to 12pt
\documentclass[11pt]{article}
\RequirePackage{amsmath,amsthm,amssymb,latexsym,amsthm,verbatim,xspace,amstext,xspace,setspace}

% Here's where you edit the class, section and title information

% Set a fixed margin along all sides
\usepackage[margin=1in, nohead, pdftex]{geometry}
\usepackage{enumerate,graphicx}
% Re-adjust the top margin if desired
\topmargin -0.2in
% These packages used for spacing in the header and throughout


% This next command affects the page numbering.  "empty" is best for short handouts
\pagestyle{empty}

% Uncomment one of the following to set the spacing to single, 1.5 or double spacing
\singlespacing
%\onehalfspacing
%\doublespacing

% This prevents paragraphs from begin indented.  Comment it out to have indentation.
\parindent 0ex
\setlength{\textheight}{9.5in}
% Finally we start!
\begin{document}

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% This is the "header" at the top.  You shouldn't have to edit these lines!
% Instead, chance the Class, Section and Title above.
\begin{center}{ \Large{Worksheet}  \\\large{9/7/2017} }\end{center}
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% At this point, you might have some introductory text, or jump straight
% into an ``enumerate'' environment for the problem statements.
\bigskip
\begin{enumerate}
\item Given vectors $\vec{a}=\langle 1,-1,0\rangle$ and $\vec{b}=\langle -2,1,3\rangle$. \begin{enumerate}[i)]\item Compute $\lVert 3\vec{a}-2\vec{b}\rVert$.\item Find $\alpha$ so that vector $\vec{a}+\alpha\vec{b}$ is collinear with vector $\vec{c}=\langle -6,2,12\rangle$.\end{enumerate}
\vspace{3in}
\item Given vectors $\vec{a}=\langle 1,0,1\rangle$, $\vec{b}=\langle 0,-1,1\rangle$, $\vec{c}=\langle 1,2,1\rangle$. Compute\begin{enumerate}[i)]\item $\vec{a}\cdot\vec{b}$\item $(\vec{a}\times\vec{b})\cdot\vec{c}$\item $(\vec{a}\times\vec{b})\times\vec{c}$\end{enumerate}
\newpage\item Compute the area of the shaded triangle in the following picture. Also, compute the angles of the triangle.
\begin{figure}[h]
 \centering
  \includegraphics[width=0.5\textwidth]{area}
\end{figure}
\vspace{3.5in}
\item Write the parametric equation of the line passing through the points $A = (1,0,1)$ and $B = (1,-1,2)$. Can you determine the intersection of this line and the plane $z=0$?
\end{enumerate}

\end{document}











