If in a triangle ABC, ^3A+ ^3B+ ^3C=3 A B C, then what is the value of the determinant vmatrix a&b&c &c&a &a&b vmatrix ; where a, b, c are sides of the triangle?

NDA 2024 Mathematics question

If in a triangle , , then what is the value of the determinant ; where are sides of the triangle?

Answer: (D)

By the sine rule etc., so the condition becomes . The determinant equals

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Question ID VK-029809