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Let \( \vec{p}, \vec{q}, \vec{r} \) be three mutually perpendicular vector
\( \mathrm{P} \) of the same magnitude. If a vectors \( \vec{x} \) satisfies the

W equation
\[
\overrightarrow{\mathrm{p}} \times[(\overrightarrow{\mathrm{x}}-\overrightarrow{\mathrm{q}}) \times \overrightarrow{\mathrm{p}}]+\overrightarrow{\mathrm{q}} \times[(\overrightarrow{\mathrm{x}}-\overrightarrow{\mathrm{r}}) \times \overrightarrow{\mathrm{q}}]+
\]
\( \overrightarrow{\mathrm{r}} \times[(\vec{x}-\vec{p}) \times \overrightarrow{\mathrm{r}}]=\overrightarrow{0} \), then \( \vec{x} \) is given by
(1) \( \frac{1}{2}(\overrightarrow{\mathrm{p}}+\overrightarrow{\mathrm{q}}-2 \overrightarrow{\mathrm{r}}) \)
(2) \( \frac{1}{2}(\vec{p}+\vec{q}+\overrightarrow{\mathrm{r}}) \)
(3) \( \frac{1}{3}(\vec{p}+\overrightarrow{\mathrm{q}}+\overrightarrow{\mathrm{r}}) \)
(4) \( \frac{1}{3}(2 \vec{p}+\overrightarrow{\mathrm{q}}-\overrightarrow{\mathrm{r}}) \)
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