The value of `| [a,b,c], [b,c,a], [c,a,b]|`

If a ,b ,c are sides of a scalene triangle, then value of |[a, b, c] ,[b, c, a] ,[c, a, b]| is positive (b) negative non-positive (d) non-negative

The product of all values of t , for which the system of equations (a-t)x+b y+c z=0,b x+(c-t)y+a z=0,c x+a y+(b-t)z=0 has non-trivial solution, is (a) |[a, -c, -b], [-c, b, -a], [-b, -a, c]| (b) |[a, b, c], [b, c, a], [c, a, b]| (c) |[a, c, b], [b, a, c], [c, b, a]| (d) |[a, a+b, b+c], [b, b+c, c+a], [c, c+a, a+b]|

The value of |(b +c,a,a),(b,c +a,b),(c,c,a +b)| , is

Let a ,b ,c be positive and not all equal. Show that the value of the determinant |[a, b, c],[b, c, a],[ c, a ,b]| is negative.

If a,b,c are in G.P. then the value of |(a,b,a+b),(b,c,b+c),(a+b,b+c,0)|= (A) 1 (B) -1 (C) a+b+c (D) 0

Prove that: |[b, c-a^2,c] ,[a-b^2,a b-c^2,c ],[a-b^2,a ,b-c^2b c-a^2a b-c^2b c-a^2c a-b^2]|=|[a, b, c],[ b ,c ,a],[ c, a ,b]|^2 .

If |a|=1,|b|=3 and |c|=5 , then the value of [a-b" "b-c" "c-a] is

If f(x)=a+b x+c x^2AAa ,b ,c in R and a ,b ,c are distinct, then value of |a b c b c a c a b| is (where omega&omega^2 are complex cube roots of unity) f(1)f(omega)f(omega^2) (b) -f(omega)f(omega^2) -f(1)f(omega)f(omega^2) (d) f(omega)f(omega^2)

The value of |(a-b,b+c,a),(b-a,c+a,b),(c-a,a+b,c)| is

The value of |{:(1+a,b,c),(a,1+b,c),(a,b,1+c):}| is