` if triangle = [[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]|=

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

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

If Delta=|[a_1,b_1,c_1],[a_2,b_2,c_2],[a_3,b_3,c_3]| and A_1,B_1,C_1 denote the co-factors of a_1, b_1, c_1 respectively, then the value of the determinant |[A_1,B_1,C_1],[A_2,B_2,C_2],[A_3,B_3,C_3]| is-

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]|

Let vec a = a_1 hat i + a_2 hat j+ a_3 hat k;vec b = b_1 hat i+ b_2 hat j+ b_3 hat k ; vec c= c_1hat i + c_2 hat j+ c_3 hat k be three non-zero vectors such that vec c is a unit vector perpendicular to both vec a & vec b. If the angle between vec a and vec b is pi/6 , then |(a_1,b_1,c_1),(a_2,b_2,c_2),(a_3,b_3,c_3)|^2=

Three linear equations a_1x+b_1y+c_1z=0, a_2x+b_2y+c_2z=0,a_3x+b_3y+c_3z=0 are consistent if (A) |(a_1,b_1,c_1),(a_2,b_2,c_2),(a_3,b_3,c_3)|=0 (B) |(a_1,b_1,c_1),(a_2,b_2,c_2),(a_3,b_3,c_3)|=-1 (C) a_1b_1c_1+a_2b_2c_2+a_3b_3c_3=0 (D) none of these

If delta =|(a_1,b_1,c_1),(a_2,b_2,c_2),(a_3,b_3,c_3)| then the value of |(2a_1+3b_1+4c_1,b_1,c_1),(2a2+3b_2+4c_2,b_2,c_2),(2a_3+3b_3+4c_3,b_3,c_3)| is equal to