Summary: This paper further develops conformal geometric algebra (CGA) from both the algebraic aspect and the geometric viewpoint by exploring the algebraic properties and geometric interpretations of the graded monomials generated by null vectors. The content includes the computation of the orientations of various dimensional spheres and planes, the trigonometry of long brackets, the graded null monomial representation of angles and directions, the geometric meaning of various single-graded null monomials, etc. These results help not only in understanding the geometric implication of various advanced symbolic algebraic manipulations in conformal geometric algebra, but also in clarifying the intrinsic machinery behind the efficiency brought about by conformal geometric algebra in symbolic geometric computing.