Under which of the following conditions does the determinant vmatrix a&b&c &c&a &a&b vmatrix vanish? 1. a+b+c=0 2. a^3+b^3+c^3=3abc 3. a^2+b^2+c^2-ab-bc-ca=0 Select the correct answer using the code given below :

NDA 2022 Mathematics question

Under which of the following conditions does the determinant vanish? 1. 2. 3. Select the correct answer using the code given below :

Answer: (D)

The determinant equals 3abc-a^3-b^3-c^3 = -(a+b+c)(a^2+b^2+c^2-ab-bc-ca). It vanishes when

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Question ID VK-029294