Let $\overline{\mathrm{a}}, \overline{\mathrm{b}}, \overline{\mathrm{c}}$ be three vectors mutually perpendicular to each other and have same magnitude. If a vector $\overrightarrow{\mathrm{r}}$ satisfies $\overrightarrow{\mathrm{a}}\times \left\{\left(\overrightarrow{\mathrm{r}}-\overrightarrow{\mathrm{b}}\right)\times \overrightarrow{\mathrm{a}}\right\}+\overrightarrow{\mathrm{b}}\times \left\{\left(\overrightarrow{\mathrm{r}}-\overrightarrow{\mathrm{c}}\right)\times \overrightarrow{\mathrm{b}}\right\}+\overrightarrow{\mathrm{c}}\times \left\{\left(\overrightarrow{\mathrm{r}}-\overrightarrow{\mathrm{a}}\right)\times \overrightarrow{\mathrm{c}}\right\}=0 \mathrm{then} \overrightarrow{\mathrm{r}}$ is equal to