\( \vec{p}, \vec{q} \), and \( \vec{r} \) are three mutually perpendicular vectors of the same m...
\( \vec{p}, \vec{q} \), and \( \vec{r} \) are three mutually perpendicular vectors of the same magnitude. If vector \( \vec{x} \) satisfies the equation \( \vec{p} \times((\vec{x}-\vec{q}) \times \vec{p})+\vec{q} \times((\vec{x}-\vec{r}) \times \vec{q})+\vec{r} \times((\vec{x}-\vec{p}) \times \vec{r}=\overrightarrow{0} \) then \( \vec{x} \) is given by
(a) \( \frac{1}{2}(\vec{p}+\vec{q}-2 \vec{r}) \)
(b) \( \frac{1}{2}(\vec{p}+\vec{q}+\vec{r}) \)
(c) \( \frac{1}{3}(\vec{p}+\vec{q}+\vec{r}) \)
(d) \( \frac{1}{3}(2 \vec{p}+\vec{q}-\vec{r}) \)
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