If `a!=b!=c` such that `|[a^3-1,b^3-1,c^3-1] , [a,b,c] , [a^2,b^2,c^2]|=0` then

Select and write the correct answer from the given alternatives in each of the following:If a!=b!=c!=0 such that |(a^3-1,b^3-1,c^3-1),(a,b,c),(a^2,b^2,c^2)|=0

If a, b, c are the sides of a scalene triangle such that |[a , a^2 , a^(3)-1 ],[b , b^2 , b^(3)-1],[ c, c^2 , c^(3)-1]|=0 , then the geometric mean of a, b c is

If b ne c and |[a , a^2, 1+a^3],[ b, b^2, 1+b^3],[ c, c^2, 1+ c^3]| =0 then prove that a b c =-1

Suppose a,b,c, gt0 and |(a^(3)-1,a^(2),a),(b^(3)-1,b^(2),b),(c^(3)-1,c^(2),c)|=0 then least possible value of a+b+c is ____________

|[a,a^2,a^3-1],[b,b^2,b^3-1],[c,c^2,c^3-1]|=0 prove that abc= I

If |[a_1,b_1,c_1] , [a_2,b_2,c_2] ,[a_3,b_3,c_3]|=5; then the value of |[b_2c_3-b_3c_2,c_2a_3-c_3a_2,a_2b_3-a_3b_2] , [b_3c_1-b_1c_3,c_3a_1-c_1a_3,a_3b_1-a_1b_3] , [b_1c_2-b_2c_1,a_2c_1-a_1c_2,b_2a_1-b_1a_2]|

If A=|(1,1,1),(a,b,c),(a^3,b^3,c^3)|, B=|(1,1,1),(a^2,b^2,c^2),(a^3,b^3,c^3)|, C=|(a,b,c),(a^2,b^2,c^2),(a^3,b^3,c^3)| , then which relation is correct :