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{\bf HW 2\\Math 261, F18}

Please see the course syllabus for details on how to turn in your homework assignments.  This one is due at the beginning of your class on \underbar{\bf Friday, September 7}.


\begin{enumerate}

\item Determine the equation of the plane that passes through points $(0,1,0)$, $(-1,0,1)$, and $(0,-2,1)$.  Please give your answer in the form
$$\raisebox{-2pt}{\framebox(10,10){}} \ x + \raisebox{-2pt}{\framebox(10,10){}} \ y + \raisebox{-2pt}{\framebox(10,10){}} \ z = 1.$$


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\item Fill in the blanks of the following parameterization of a line through the points $P_1 = (1,1,0)$ and $P_2 = (0,3,1)$:
$$
\begin{cases}
x=-1+t\\
y=\raisebox{-2pt}{\framebox(10,10){}}+\raisebox{-2pt}{\framebox(10,10){}} \ t\\
z=\raisebox{-2pt}{\framebox(10,10){}}+\raisebox{-2pt}{\framebox(10,10){}} \ t\\
\end{cases}
$$

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\item The line given by the parameterization
$$
\begin{cases}
x=1+t\\
y=3t\\
z=2-2t\\
\end{cases}
$$
and the plane given by $x+2y+z=8$ intersect in a point.  Find that point.

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\item Compute the derivative $\mathbf r'(t)$ of vector function $\mathbf r(t) = \left\langle e^t, 3t^2 - 2t + 5, \sin(t) \right\rangle$.

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\item Suppose a particle moves according to the position function $\mathbf r(t) = \left\langle t^3, t^2, 4t+1\right\rangle$.  Determine the acceleration $\mathbf a(2)$ of the particle at $t=2$.


\end{enumerate}

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