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I am given $\vec r=x_i\hat e_i$ where $r=|\vec r|$ and the tensors are introduced as: $\overline{\overline{T}}=\frac{\delta_{ij}\hat e_i\hat e_j}{r}+\frac{x_ix_j \hat e_i\hat e_j}{r^3}$ and $\overline{\overline{A}}=\epsilon_{ijk}\frac{\delta}{\delta x_k}(\frac{1}{r})\hat e_i\hat e_j$. I am asked to calculate the $\overline{\overline{A}}$.$\overline{\overline{T}}$ and $\overline{\overline{A}}$..$\overline{\overline{T}}$ which means dot and double dot of these two tensors. I know how to get the expressions, but I am not sure how much I can simplify them. I would appreciate any suggestions regarding that.

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