Let \( \vec{a}, \vec{b}, \vec{c} \) be three vectors mutually perpendicular to each other and have same magnitude. If a …

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

\(\vec{a}\times {(\vec{r}-\vec{b})\times \vec{a}}+\vec{b}\times {(\vec{r}-\vec{c})\times \vec{b}}+\vec{c}\times {(\vec{r}-\vec{a})\times \vec{c}}=\vec{0},\)

then \( \vec{r} \) is equal to:

[JEE Main 2021, 31 Aug (Shift 2)]