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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
Δ=pqr(a3+b3+c3)abc(p3+q3+r3)
But a+b+c=0(a+b)3=c2
a3+b3+3ab(a+b)+c3=0
a3+b3+c3=3ab(c)=3abc
Similarly p3+q3+r3=3pqr
Thus Δ=pqr(3abc)abc(3pqr)=0

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