If the vectors a = i +a j +a² k , b = i +b j +b² k and c = i +c j +c² k are three non-coplanar vectors and | array lll a & a² & 1+a³ b & b² & 1+b³ c & c² & 1+c³ array |=0 , then the value of a b c is

Step-by-step solution

Since, a , b , and c are non-coplanar vectors, therefore [ a b c ] 0 = | array lll 1 & a & a² 1 & b & b² 1 & c & c² array | 0 0 array l Now, & ( array lll a & a² & 1+a³ b & b² & 1+b³ c & c² & 1+c³ array =0 . | array lll a & a² & 1 b & b² & 1 c & c² & 1 array |+ | array lll a & a² & a³ b & b² & b³ c & c² & c³ array |=0 & (1+a b c)=0 array a b c=-1