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\begin{center}
{\Large TEST 1

Math 2210}
\end{center}

\begin{itemize}
\item  You have 1 hour to complete this exam.
\item  Show all your work (and make it neat!).  
  If I can't follow your work or it is missing you WILL NOT get credit.
\item  You can use a $4 \times 6$ note card of notes.
\item  If you run out of space, use the back of these sheets.
\end{itemize}


\vspace{.4in}

Name: \hrulefill


\begin{enumerate}

\item (10 points)
  \begin{enumerate}
  \item  Write a parametric equation of the line containing the points $(1,2,3)$ and $(3, -1, 4)$.
  \item  Find the distance between the line above and the point $(1,4,8)$.
  \end{enumerate}



\item  (10 points)
	\begin{enumerate}
	\item  Compute the vector projection of the vector $\mbf{u}=(a,b,c)$ onto the vector $\mbf{i}=(1,0,0)$:
		  $\mathrm{Pr}_\mbf{i} \mbf{v}$.  Explain your answer graphically.
	\item  Generalize this and explain what vector projection is (graphically) when projecting to the vectors
		$\mathbf{j}=(0,1,0)$ and $\mathbf{k}=(0,0,1)$.
	\end{enumerate}

\item  (10 points)
	Consider the line given by the parametric equation:
  \[
  \mbf{r}(t) = \left(3-2t, -5+t, 7+3t \right)
  \]
  Find the equation of the plane that contains the line $\mbf{r}(t)$ and the point $(10, -9, -2)$.


\item  (10 points)
	Consider the curve $y=\ln x$.
  \begin{enumerate}
  \item  Write the curve as a parametric equation.
  \item  For your parametrization, find an expression for speed.
  \item  Find an expression for the curvature at an arbitrary point.
  \item  Find a general expression for the unit tangent vector and the unit normal vector.
  \item  Find a general expression for the tangential acceleration and the normal acceleration.
  \end{enumerate}





\end{enumerate}

\end{document}







