Q. Homogeneous Representation of Points and Lines in Projective Space:- Note :- all explanations should be applied to 3D projective space:-

(a) How can points and lines be represented in R2? How are they represented in P 2? How are points and planes represented in R3?

(b) Explain the geometric meaning in 2D projective space of the homogeneous representation of lines and points (Hint: Take the homogeneous representation as 3D entities and try to project these entities into 2D space).

(c)How can the direction of a line and its distance to the origin be determined?

(d) Explain geometrically that a point p that lies on a line l satisfies pTl = 0.

(e) Intersecting two lines gives a point p in 2D. How can p be determined in R2 and P 2?