If a =2 i + j -3 k , b = i -2 j + k c =- i + j -4 k and d = i + j + k , then |( a b ) ( c d )|=

Step-by-step solution

Given that, a =2 i + j -3 k b = i -2 j + k c =- i + j -4 k and d = i + j + k Now, a b = | array ccc i & j & k 2 & 1 & -3 1 & -2 & 1 array | aligned & = i (1-6)- j (2+3)+ k (-4-1) a b & =-5 i -5 j -5 k aligned Now, aligned c d & = | array ccc i & j & k -1 & 1 & -4 1 & 1 & 1 array | & = i (1+4)- j (-1+4)+ k (-1-1) & =5 i -3 j -2 k aligned Now, aligned ( a b ) ( c d )= | array ccc i & j & k -5 & -5 & -5 5 & -3 & -2 array | = i (10-15)- j (10+25)+ k (+15+25) =-5 i -35 j +40 k =5(- i -7 j +8 k ) aligned aligned |( a b )