Question:

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

Updated On: Apr 27, 2024
  • (A) 0
  • (B) 1
  • (C) pa + qb + rc
  • (D) None of these
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The Correct Option is A

Solution and Explanation

Explanation:
We have Δ=pqr(a3+b3+c3)−abc(p3+q3+r3)But a+b+c=0⇒(a+b)3=−c3⇒a3+b3+3ab(a+b)+c3=0⇒a3+b3+c3=−3ab(−c)=3abcSimilarly, p3+q3+r3=3pqrThus, Δ=pqr(3abc)−abc(3pqr)=0

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