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Question

If p + q + r = a + b + c = 0, then the determinant
Δ=∣ ∣paqbrcqcrapbrbpcqa∣ ∣ equals


A

0

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B

1

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C

pa + qb + rc

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D

none of these

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Solution

The correct option is A

0


We have Δ=pqr (a3+b3+c3)abc(p3+q3+r3)
But a + b + c = 0
(a+b)3=c3a3+b3+3ab(a+b)+c3=0a3+b3+c3=3ab(c)=3abc
Similarly, p3+q3+r3=3pqr
Thus, Δ = pqr (3 abc) - abc (3pqr) = 0
Hence the correct option is (a)


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