If the vectors $(-bc,b^2+bc,c^2+bc),(a^2+ac,-ac,c^2+ac)$ and  $(a^2+ab,b^2+ab,-ab)$ are coplanar , where none of a,b or c is zero then

$\left|\begin{array}{ccc}-bc& b^2+bc& c^2+bc\\ a^2+bc& -ac& c^2+ac\\ a^2+ab& b^2+ab& -ab\end{array}\right|=\left|\begin{array}{ccc}\frac{-bc}{a}& b+c& c+b\\ a+c& \frac{-ac}{b}& c+a\\ a+b& a+b& \frac{-ab}{c}\end{array}\right|=\left|\begin{array}{ccc}-bc& ab+ac& ac+ab\\ ab+bc& -a& ab+bc\\ ac+bc& ac+bc& -ab\end{array}\right|={(ab+bc+ca)}^3$