Let a, b, c be three vectors mutually perpendicular to each other and have same magnitude. If a vector r satisfies a ×{( r - b ) × a }+ b ×{( r - c )…

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