please share some good tutorials on projective coordinate system. 

i am stuck on moon math manual chapter 5 for about a month now. basically everything makes sense until the projective plane comes into picture

Chapter 2.1 of Graham Ellis’s “Rings and Fields” gives a great visual demonstration of what you’re looking for imo. Algebraic geometry is pretty abstract though to begin with so still may take a bit of time to understand

Faculty at IIT Bombay,  https://www.respectedsir.com/cv

"Rational Points on Elliptic Curves" by Silverman & Tate has an appendix on projective geometry. Just the details required to understand elliptic curves.

Chapter 7 of "Modern Cryptography and Elliptic Curves" by Thomas R. Shemanske has a student-friendly treatment of curves in projective space.

"Pairings for beginners" might be helpful. https://static1.squarespace.com/static/5fdbb09f31d71c1227082339/t/5ff394720493bd28278889c6/1609798774687/PairingsForBeginners.pdf

thanks! i skimmed it a bit but decided to revisit later after completing mm manual