“1) Find PQ,PR,PS: two of these have to be adjacent sides of a quadrilateral.”
I obviously meant a space (non-planar) quadrilateral since we are talking about points in R3. quadri-four, lateral-side.
However, if that bothers you, Any two lines emanating from a point are sides of some (plane) quadrilateral(s): by elementary geometry.
Either one works.
I find it hard to believe that this has to be explained to you.