If a = i -2 j -3 k , b =2 i + j - k , c = i +3 j -2 k , then [( a b ) ( b c )( b c ) ( c a )( c a ) ( a b )]=

Step-by-step solution

We have, aligned & a = i -2 j -3 k & b =2 i + j - k & c = i +3 j -2 k aligned Now, aligned & ( a b ) ( b c )=[ a b c ] b -[ a b b ] c =[ a b c ] b & ( b c ) ( c a )=[ b c a ] c -[ b c ] a =[ a b c ] c & ( c a ) ( a b )=[ c a b ] a -[ c a a ] b =[ a b c ] a & Now, [ a b c ]= [ array ccc 1 & -2 & -3 2 & 1 & -1 1 & 3 & -2 array . & =1(-2+3)+2(-4+1)-3(6-1)=1-6-15=-20 aligned aligned & [( a b ) ( b c )( b c ) ( c a ) & = [ array ll -20 b -20 c -20 a ] ( c a ) ( a b )] array . & = | array ccc -40 & -20 & 20 -20 & -60 & 4