If  $\stackrel{-}{a},\stackrel{-}{b},\stackrel{-}{c}$ are unit coplanar vectors ,then the scalar triple product of  $\left[\begin{array}{ccc}2\overline{a}-\overline{b}& 2\overline{b}-\overline{c}& 2\overline{c}-\overline{a}\end{array}\right]$

since

$\begin{array}{l}\stackrel{-}{a},\stackrel{-}{b},\stackrel{-}{c}arecoplane\left[\stackrel{-}{a}\stackrel{-}{b}\stackrel{-}{c}\right]=0\\ \stackrel{-}{\begin{array}{l}Let\stackrel{-}{\alpha }=2\stackrel{-}{a}-\stackrel{-}{b}\stackrel{-}{c},\stackrel{-}{\beta }=2\stackrel{-}{b}-\stackrel{-}{c}and\stackrel{ }{\gamma =2\stackrel{-}{c}-\stackrel{-}{a}then}\\ \left[\stackrel{-}{\alpha }\stackrel{-}{\beta }\stackrel{-}{\gamma }\right]=\left|\begin{array}{l}2-10\\ 02-1\\ -102\end{array}\right|\times \left[\stackrel{-}{a}\stackrel{-}{b}\stackrel{-}{c}\right]=7\left[\stackrel{-}{a}\stackrel{-}{b}\stackrel{-}{c}\right]=0\end{array}}\end{array}$