Question

If p + q + r = 0 = a + b + c, then value of the determinant

$\left| \begin{matrix} pa & qb & rc \\ qc & ra & pb \\ rb & pc & qa \end{matrix} \right|$ is –

• A. 0
• B. pa + qb + rc
• C. 1
• D. None of these

Answer 1

Answer: (A)

0

Answer 2

D = pqr (a³ + b³ + c³) – a b c (p³ + q³ + r³)

If $\begin{Bmatrix} p + q + r = 0 \Rightarrow p^{3} + q^{3} + r^{3} = 3pqr \\ a + b + c = 0 \Rightarrow a^{3} + b^{3} + c^{3} = 3abc \end{Bmatrix}$

\ D = pqr (3 abc) – abc (3 pqr)

\ D = 0