If $p+q+r=0$  and  $\left|\begin{array}{ccc}pa& qb& rc\\ qc& ra& pb\\ rb& pc& qa\end{array}\right|=k \left|\begin{array}{ccc}a& b& c\\ b& c& a\\ c& a& b\end{array}\right|$   then the value of K is

$\begin{array}{l}Pqr\left(a^3+b^3+c^3\right)-abc\left(p^3+q^3+r^3\right)\\ \Rightarrow pqr\left(a^3+b^3+c^3-3abc\right)-abc\left(p^3+q^3+r^3-3pqr\right)\\ \Rightarrow pqr\left(a^3+b^3+c^3-3abc\right)-abc\left(p-q+r\right)\left(p^2+q^2+r^2-pq-qr-rp\right)\\ =pqr\left(a^3+b^3+c^3-3abc\right)\end{array}$