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\begin{center}
  18.022 Recitation Quiz \iftoggle{solutions}{(with solutions)}{} \\
  15 September 2014 \\
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\itm Find the equation of the plane that contains the points $(1,-2,0)$,
$(3,1,4)$, and $(0,-1,2)$. 

\sol{(Taken from \textit{Paul's online math notes}) The vector
  $\overrightarrow{PQ} \times \overrightarrow{PR} = (2,-8,5)$ is orthogonal
  to $\overrightarrow{PQ}$ and $\overrightarrow{PR}$ and therefore also to
  the desired plane. So the plane consists of all points $S = (x,y,z)$
  which satisfy the equation $(2,-8,5)\cdot \overrightarrow{PS} = 0$, which
  simplifies to $\boxed{2x - 8y + 5z = 18}$.}{}

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