if `Delta=|[a_1,b_1,c_1],[a_2,b_2,c_2],[a_3,b_3,c_3]|`

If in the determinant Delta=|[a_1,b_1,c_1],[a_2,b_2,c_2],[a_3,b_3,c_3]|,A_1,B_1,C_1 etc. be the co-factors of a_1,b_1,c_1 etc., then which of the following relations is incorrect-

If A_1, B_1, C_1,... are respectively the co-factors of the elements a_1,b_1, c_1,... of the determinant Delta=|[a_1, b_1,c_1] , [a_2, b_2, c_2] , [a_3, b_3,c_3]| then |[B_2,C_2] , [B_3,C_3]|=

Consider the determinant Delta = |[a_1+b_1x^2,a_1x^2+b_1,c_1],[a_2+b_2x^2,a_2x^2+b_2,c_2],[a_3+b_3x^2,a_3x^2+b_3,c_3]| = 0 , \ w h e r e \ a_i ,b_i , c_i in R \ (i = 1,2,3) \ a n d \ x in R . Statement 1: The value of x satisfying Delta=0 are x=1,-1. Statement 2: If |[a_1,b_1,c_1],[a_2,b_2,c_2],[a_3,b_3,c_3]|=0,t h e n \ Delta=0.

Consider the determinant Delta = |[a_1+b_1x^2,a_1x^2+b_1,c_1],[a_2+b_2x^2,a_2x^2+b_2,c_2],[a_3+b_3x^2,a_3x^2+b_3,c_3]| = 0 , \ w h e r e \ a_i ,b_i , c_i in R \ (i = 1,2,3) \ a n d \ x in R . Statement 1: The value of x satisfying Delta=0 are x=1,-1. Statement 2: If |[a_1,b_1,c_1],[a_2,b_2,c_2],[a_3,b_3,c_3]|=0,t h e n \ Delta=0.

If a_mhati+b_mhatj+c_mhatk m=1,2,3 are pairwise perpendicular unit vectors then |[a_1,b_1,c_1] , [a_2,b_2,c_2] , [a_3,b_3,c_3]| is equal to

Show that [[a_1,b_1,-c_1],[-a_2,b_2,c_2],[a_3,b_3,-c_3]]= [[a_1,b_1,c_1],[a_2,b_2,c_2],[a_3,b_3,c_3]]

If A=[[a_1,b_1,c_1],[a_2,b_2,c_2],[a_3,b_3,c_3]] and B=[[ c_1,c_2,c_2],[a_1,a_2,a_3],[b_1,b_2,b_3]] then

Show that by eliminating alpha and beta from the equations. a_ialpha+b beta_i+c_i =0, i=1,2,3 we get [[a_1,b_1,c_1],[a_2,b_2,c_2],[a_3,b_3,c_3]] =0

Let veca = a_1hati + a_2hatj + a_3hatk, vecb = b_1hati + b_2hatj+ b_3hatk and vecc = c_1hati + c_2hatj + c_3hatk be three non zero vectors such that |vecc| =1 angle between veca and vecb is pi/4 and vecc is perpendicular to veca and vecb then |[a_1, b_1, c_1], [a_2, b_2, c_2], [a_3, b_3, c_3]|^2= lamda(a_1 ^2 +a_2 ^2 + a_3 ^2)(b_1 ^2 + b_2^2+b_3^2) where lamda is equal to (A) 1/2 (B) 1/4 (C) 1 (D) 2

Delta=|{:(a_1,b_1,c_1),(a_2,b_2,c_2),(a_3,b_3,c_3):}|and Delta'|{:(A_1,B_1,C_1),(A_2,B_2,C_2),(A_3,B_3,C_3):}| where A_1,B_1,C_1,A_2,B_2,……… are respectively the cofactors of the elements a_1,b_1,c_1,a_2,b_2,….. of the determinant then Delta'=........