aligned & If a = i + j + k , b =2 i - j +3 k and c = i - j & and if 6 i +2 j +3 k = ₁( a b ) & + ₂( b c )+ ₃( c a ) , then ( ₁, ₂, ₃ )= aligned

Step-by-step solution

Let a = i + j + k , b =2 i - j +3 k and c = i - j aligned Now, a b & = | array ccc i & j & k 1 & 1 & 1 2 & -1 & 3 array | & = i (3+1)- j (3-2)+ k (-1-2)=4 i - j -3 k aligned and b c = | array ccc i & j & k 2 & -1 & 3 1 & -1 & 0 array |= i (0+3)- j (0-3)+ k (-2+1)=3 i +3 j - k and c a = | array ccc i & j & k 1 & -1 & 0 1 & 1 & 1 array | = i (-1-0)- j (1-0)+ k (1+1)= i - j +2 k Now, 6 i +2 j +3 k = ₁( a b )+ ₂( b c ) aligned 6 i +2 j +3 k = & ₁(4 i - j -3 k ) + ₃( c a ) & ₂(3 i +3 j - k )+ ₃(- i - j +2 k ) 6 i +2 & j