If a, b, c are sides of a scalene triangle, then the value of <math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="|
Step-by-Step Solution
Key Concept: The determinant of the circulant matrix |a b c; b c a; c a b| is -(a+b+c)(a^2+b^2+c^2-ab-bc-ca) = -1/2(a+b+c)((a-b)^2+(b-c)^2+(c-a)^2). Since a, b, c are sides of a scalene triangle, a+b+c > 0 and (a-b)^2+(b-c)^2+(c-a)^2 > 0, making the expression negative.
The determinant is given by -(a+b+c)(a^2+b^2+c^2-ab-bc-ca). This can be written as -1/2(a+b+c)((a-b)^2+(b-c)^2+(c-a)^2). Since a, b, c are sides of a triangle, a+b+c > 0. Since the triangle is scalene, a, b, c are distinct, so (a-b)^2+(b-c)^2+(c-a)^2 > 0. Thus, the value is negative.
Correct Answer: 2