We consider the orbits of the group G=PGL2(q) on the points, lines and planes of the projective space PG(3, q) over a finite field Fq of characteristic different from 2 and 3. The points of PG(3, q) can be identified with projective space of binary cubic forms, and the set L of lines of PG(3, q) can be thought of as pencils of cubic forms. The action of G on PG(1, q) naturally induces an action of G on binary cubic forms f(X, Y). The points of PG(3, q) decompose into five G orbits. The G orbits on L were recently obtained by the authors. Let I be the subset of L×PG(3,q) consisting of pairs (L, P) where L is a line incident with the point P. The decomposition of L×PG(3,q) into G×G orbits yields a partition of I. The problem that we solve in this work is to determine the sizes of the corresponding parts of I.