x???
i dont understand ur question...........but i think this is wat u want.........
if p satisfies p X a = b and p.a=0 for non zero vectors a and b, then x is equal to :
#p.a=0
For non -zero vectors ,from this condition implies that "p" and "a" are perpendicular...................................eq1
#p X a = b
For non-zero vectors ,by definition of cross product,"b" is perpendicular both to "p" and "a"......................................eq2
From eq1 and eq2 we can infer that vectors "p","a" and "b" are mutually perpendicular.
I think this is what u want.............if u want any other plz specify.