Let p , q , r be three mutually perpendicular vectors of the same magnitude. If a vector…

Let \(\vec{p}, \vec{q}, \vec{r}\) be three mutually perpendicular vectors of the same magnitude. If a vector satisfies the equation
\(\vec{p} \ imes((\vec{x}-\vec{q}) \ imes \vec{p})+\vec{q} \ imes((\vec{x}-\vec{r}) \ imes \vec{q})+\vec{r} \ imes((\vec{x}-\vec{p}) \ imes \vec{r})=\overrightarrow{0}\) then is given by