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 :