$= \,2\left( {\,i\,\, + \;\,3j\,\, - \,\,2k} \right)\, + \,\,\left( {4i\,\, - \,2j\,\, + \;\,4k} \right)\,\, $
$= \,\,6i\,\, + \;\,4j$
$\vec a \,\, - \;\,2\vec b \,\, $
$= \,\,\left( {i\,\, + \;\,3j\,\, - \,\,2k} \right)\,\, - \,\,2\,\,\left( {4i\,\, - \,\,2j\,\, + \;\,4k} \right)\,\,\, $
$= \,\, - 7i\,\, + \;\,7j\,\, - \,\,10k$
તેથી $\left( {2\vec a \, + \;\,\vec b } \right).\,\,\left( {\vec a \,\, - \;\,2\vec b } \right)\,$
$ = \,\,\left( {6i\,\, + \;\,4j} \right)\,\,.\,\left( { - 7i\,\, + \;\,7j\,\, - \,\,10k} \right)\,\,$ $ = \,\,\left( 6 \right)\,\,\left( { - 7} \right)\,\, + \,\,\left( 4 \right)\,\,\left( 7 \right)\,\, + \;\,\left( 0 \right)\,\,\left( { - 10} \right) $
$= - 42\,\, + \;\,28\,\, = \,\, - 14$
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