a
$\vec a \,\, \times \,\,\left( {\,\vec b \, \times \,\vec c } \right)\, = \,\left( {\vec a .\,\,\vec c } \right)\,\vec b \,\, - \,\,\left( {\vec a \,.\,\vec b } \right)\,\,\vec c $
$\vec a .\,\,\vec c \,\, = \,\,\left( 1 \right)\,\,\left( 1 \right)\,\, + \;\,\left( 2 \right)\,\,\left( 3 \right)\,\, + \;\,\left( { - 2} \right)\,\,\left( { - 1} \right)\,\, = \,\,9$
$\vec a \,.\,\vec b \,\, = \,\,\left( 1 \right)\,\,\left( 2 \right)\,\, + \;\,\left( 2 \right)\,\,\left( { - 1} \right)\,\, + \;\,\left( { - 2} \right)\,\,\left( 1 \right)\,\, = \,\, - 2$
$\therefore \,\,\vec a \, \times \,\,\left( {\vec b \,\, \times \,\,\vec c \,} \right)\,\,$
$ = \,\,\left( 9 \right)\,\,\left( {2\hat i\,\, - \,\hat j\,\, + \;\,\hat k} \right)\,\, - \,\,\left( { - 2} \right)\,\,\left( {\hat i\,\, + 3\hat j\,\, - \;\,\hat k} \right)$
$ = \,\,18\hat i\,\, - \,9\hat j\,\, + \;\,9\hat k\,\, - \,\,\left( { - 2\hat i\,\, - \,6\hat j\,\, + \;\,2\hat k} \right)\,\, $
$= \,\,20\hat i\,\, - \,3\hat j\,\, + \;\,7\hat k$