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If $\overrightarrow a,\overrightarrow b,\overrightarrow c$ are three non coplanar vectors then $(\overrightarrow a+\overrightarrow b+\overrightarrow c).(\overrightarrow b+\overrightarrow c)\times (\overrightarrow c+\overrightarrow a)=?$

$\begin{array}{1 1} =[\overrightarrow a\:\overrightarrow b\:\overrightarrow c] \\ =2[\overrightarrow a\:\overrightarrow b\:\overrightarrow c] \\ 0 \\ =-[\overrightarrow a\:\overrightarrow b\:\overrightarrow c]\end{array}$

Can you answer this question?

$(\overrightarrow a+\overrightarrow b+\overrightarrow c).(\overrightarrow b+\overrightarrow c)\times (\overrightarrow c+\overrightarrow a)=\left|\begin {array}{ccc}1 & 1& 1\\0 & 1 & 1\\1 & 0 & 1\end {array}\right| [\overrightarrow a\:\overrightarrow b\:\overrightarrow c]$
$=[\overrightarrow a\:\overrightarrow b\:\overrightarrow c]$
answered Nov 21, 2013