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

Step-by-step solution

aligned & ( a - b ) [( a b ) ( a c )] & =( a - b ) [ a b c ] a -[ a b a ] c & =( a - b ) a [ a b c ] & =( a a - b a )[ a b c ] aligned aligned & = (1^2+1^2+1^2 )-(-1+2-2) | array ccc 1 & 1 & 1 -1 & 2 & -2 2 & -1 & 2 array | & =4 | array ccc 1 & 0 & 0 -1 & 3 & -1 2 & -3 & 0 array | & =4 1 (0-3)=-12 aligned