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Question: If a, b, c are non zero real numbers, then \(\left| \begin{matrix} bc & ca & ab \\ ca & ab & bc \\ a...

If a, b, c are non zero real numbers, then ∣bccaabcaabbcabbcca∣\left| \begin{matrix} bc & ca & ab \\ ca & ab & bc \\ ab & bc & ca \end{matrix} \right|

vanishes when

A

1a−1b−1c\frac{1}{a} - \frac{1}{b} - \frac{1}{c} = 0

B

1a+1b+1c\frac{1}{a} + \frac{1}{b} + \frac{1}{c} = 0

C

1b−1c−1a\frac{1}{b} - \frac{1}{c} - \frac{1}{a} = 0

D

1b−1c+1a\frac{1}{b} - \frac{1}{c} + \frac{1}{a}= 0

Answer

1a+1b+1c\frac{1}{a} + \frac{1}{b} + \frac{1}{c} = 0

Explanation

Solution

3(bc)(ca)(ab) – [(ab)3 + (bc)3 + (ca)3] = 0

Ž (ab + bc + ca)[(ab)2 + (bc)2 + (ca)2 – ab2c – bc2a – ca2b]

= 0

Ž ba + cb + ca = 0

Ž 1a\frac{1}{a}+1b\frac{1}{b} + 1c\frac{1}{c} = 0