Past exam of the mathematics course of the University of Cambridge / 2022 / iii / Paper 329 / 1 / b / Solution

Put $S(\mathbf{x})=\mathbf{x}\cdot \mathbf{A}\cdot \mathbf{x}$. Since $\mathbf{u}=-S{r}^{-5}\mathbf{x}$ and $\nabla \times \mathbf{x}=0$, the product rule givesFor the symmetric stresslet tensor $\mathbf{A}$,The final term is parallel to $\mathbf{x}$ and drops out of the cross product, leaving