Let a = i + j + k , b = i + j -2 k , c = i -2 j +3 k and d =-4 i +5 j -3 k , d =x( b c )- 7 9 ( c a )+ z ( a b ) , then x=

Step-by-step solution

b c = | array lll i & j & k 1 & 1 & -2 1 & -2 & 3 array |= i (-1)- j (5)+ k (-3) aligned & =- i -5 j -3 k & c a = | array lll i & j & k 1 & -2 & 3 1 & 1 & 1 array |= i (-5)- j (-2)+ k (3) & =-5 i +2 j +3 k & a b = | array ccc i & j & k 1 & 1 & 1 1 & 1 & -2 array |= i (-3)- j (-3)+ k (0) & =-3 i +3 j aligned Now d =x( b c )- 7 9 ( c a )+z( a b ) d =x(- i -5 j -3 k )- 7 9 (-5 i +2 j +3 k )+z(-3 i +3 j ) Since d =4 i +5 j -3 k aligned 4 i +5 j -3 k = i & (-x+ 35 9 -3 z ) & + j (-5 x- 14 9 +3 z )+ k (-3 x- 7 3 ) aligne