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{\bf Question}

Find the volume of the parallelipiped with sides given by the
vectors ${\bf a} = (1,1,-1) \hspace{.1in} {\bf b} = (1,-1,1)
\hspace{.1in} ,{\bf c} = (-1,1,1)$

\vspace{.25in}

{\bf Answer} $${\bf a} = (1,1,-1) \hspace{.1in} {\bf b} = (1,-1,1)
\hspace{.1in} ,{\bf c} = (-1,1,1)$$

vol = $|({\bf a}\times {\bf b}) \cdot {\bf c}|$

${\bf a}\times {\bf b} = ((1 \times 1) - (-1 \times -1), (-1
\times 1) - (1 \times 1), (1 \times -1) - (1 \times 1)) =
(0,-2,-2)$

${\bf a}\times {\bf a}\cdot{\bf a} = (0,-2,-2) \cdot (-1,1,1) =
-4$

Hence the volume is equal to 4.



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