Vector Algebra: JEE Main 2021 Mathematics question

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 :