\( P(\vec{p}) \) and \( Q(\vec{q}) \) are the position vectors of t...

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\( P(\vec{p}) \) and \( Q(\vec{q}) \) are the position vectors of two fixed points and \( R(\vec{r}) \) is the position vector of a
\( \mathrm{P} \) variable point. If \( R \) moves such that \( \overrightarrow{(r}-\vec{p}) \times(\vec{r}-\vec{q})=\overrightarrow{0} \), then the locus of \( R \) is
(1) a plane containing the origin \( O \) and parallel to two non-collinear vectors \( \overrightarrow{O P} \) and \( \overrightarrow{O Q} \)
(2) the surface of a sphere described on \( P Q \) as its diameter
(3) a line passing through points \( P \) and \( Q \)
(4) a set of lines parallel to line \( P Q \)
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