If `|(x +a,b,c),(a,x +b,c),(a,b,x +c)| = 0`, then x equals

If a,b,c are different and |(0,x-a,x-b),(x+a,0,x-c),(x+b,x+c,0)|=0 then x=

If (b-c)^(2)!=(a-b)(c-a) and |(a+x,b+x,c+x),(b+x,c+x,a+x),(c+x,a+x,b+x)|=0 then x=

If A=|(a, b, c), (c, a, b), (b, c, a)| and a, b, c are roots of equation x^(3)+x^(2)-4=0, then A A^(T) is equal to

If |[a,b,c],[b,a,b],[x,b,c]|=0 then x=____.

If a+b+c=0 and |{:(a-x,c,b),(c,b-x,a),(b,a,c-x):}|=0 then find the value of x

If a+b+c=0 and |(a-x,c,b),(c,b-x,a),(b,a,c-x)|=0 then x=

If a+b+c=0and|(a-x,c,b),(c,b-x,a),(b,a,c-x)|=0 , then show that either x=0 or x=pmsqrt((3)/(2)(a^(2)+b^(2)+c^(2)))

The equation |(x-a,x-b,x-c),(x-b,x-a,x-c),(x-c,x-b,x-a)|=0 (a,b,c are different) is satisfied by (A) x=(a+b+c0 (B) x= 1/3 (a+b+c) (C) x=0 (D) none of these

The equation |(x-a,x-b,x-c),(x-b,x-a,x-c),(x-c,x-b,x-a)|=0 (a,b,c are different) is satisfied by (A) x=(a+b+c0 (B) x= 1/3 (a+b+c) (C) x=0 (D) none of these