I'm given that

$\overrightarrow{E}=\frac{{\mu}_{0}{p}_{0}{\omega}^{2}}{4\pi r}{\textstyle [}\mathrm{cos}u{\textstyle (}\hat{x}-\frac{x}{r}\hat{r}{\textstyle )}+\mathrm{sin}u{\textstyle (}\hat{y}-\frac{y}{r}\hat{r}{\textstyle )}{\textstyle ]}$

implies

$-\frac{{\mu}_{0}{p}_{0}{\omega}^{2}}{4\pi r}{\textstyle [}\mathrm{cos}u\hat{x}\times \hat{r}+\mathrm{sin}u\hat{y}\times \hat{r}{\textstyle ]}=\frac{1}{c}\hat{r}\times \overrightarrow{E},$

but I don't follow how to get from the former to the latter.

$\overrightarrow{E}=\frac{{\mu}_{0}{p}_{0}{\omega}^{2}}{4\pi r}{\textstyle [}\mathrm{cos}u{\textstyle (}\hat{x}-\frac{x}{r}\hat{r}{\textstyle )}+\mathrm{sin}u{\textstyle (}\hat{y}-\frac{y}{r}\hat{r}{\textstyle )}{\textstyle ]}$

implies

$-\frac{{\mu}_{0}{p}_{0}{\omega}^{2}}{4\pi r}{\textstyle [}\mathrm{cos}u\hat{x}\times \hat{r}+\mathrm{sin}u\hat{y}\times \hat{r}{\textstyle ]}=\frac{1}{c}\hat{r}\times \overrightarrow{E},$

but I don't follow how to get from the former to the latter.