It's a vector triple product:

$\displaystyle \mathbf{r}\cdot(\mathbf{\Phi}\times\mathbf{r}).$

And what do you know about $\displaystyle \mathbf{r}$ relative to $\displaystyle \mathbf{\Phi}\times\mathbf{r}?$

What does that tell you about the dot product in the vector triple product?