Vector Algebra

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