If the vectors a , b , c are non coplanar, then [ a +2 b b +2 c c +2 a ] [ a b c ] =

Step-by-step solution

Here [ array ccc a +2 b & b +2 c & c +2 a array ] aligned [ a &+2 b b +2 c c +2 a ] &=( a +2 b ) [( b +2 c ) ( c +2 a )] &=( a +2 b ) [( b c )+(2 b a )+(2 c c )+(4 c a )] &=( a +2 b ) [( b c )+2( b a )+0+4( c a )] &=[ a ( b c )]+0+0+0+0+8[ b ( c a )] &=9[ a ( b c )] &=9 [ array lll a & b & c array ] aligned Now [ array lll a +2 b & b +2 c & c +2 a array ] [ array lll a & b & c array ] = 9[ a b c ] [ a b c ] =9