If the vectors a i + j + k ; i +b j + k ; i + j +c k ( a b c 1) are coplanar then 1 1-a + 1 1-b + 1 1-c =

Step-by-step solution

Given vectors are coplanar aligned & | array ccc a & 1 & 1 1 & b & 1 1 & 1 & c array |=0 & | array ccc a & 1 & 1 1-a & b-1 & 0 1-a & 0 & c-1 array |=0 [ array l R₂^ R₂-R₁ ; R₃ R₃-R₁ array ] & | array ccc a 1-a & 1 b-1 & 1 c-1 1 & 1 & 0 1 & 0 & 1 array |=0 & | array ccc a 1-a & 1 b-1 & 1 c-1 1 & 1 & 0 0 & -1 & 1 array |=0 [ Applying R₃ R₃-R₂ ] & a 1-a - ( 1 b-1 + 1 c-1 )=0 & 1 1-a -1+ 1 1-b + 1 1-c =0 1 1-a + 1 1-b + 1 1-c =1 aligned