Coordinate Geometry, 3D, and Vectors

This is usually counted among the tough topics. Because it involves a lot of formulae and calculations(at times) and hence costs a lot of time during exam. You might wanna be very fast in calculations before moving here. So prepare your algebra well!

So, the topics will be 

1. Straight Line and Basics- This is the most important chapter because this forms the basis of other chapters. There would be various forms of lines, and you must be familiar with each and everyone of them. There would be lots of definitions in this chapter(orthocentre,incentre,etc.)Lots of formulae, learn them all by heart.  Shift of origin and family of lines are two important topics which will help you solve questions fast. Practice a lot, and different types of question, don't solve 10 questions of the same type. Solve 10 questions of 10 types(i.e.1-2 questions of each type).

2. Circles and Conic sections- You must be well prepared with formulae of equations in standard form, parametric form, positions of foci, vertices, length of latus rectum,etc. tangent, normal, etc. Joint equation of curves and lines is very helpful at times. There are a few special results(e.g. reflection properties of parabola and ellipse). It's tough to remember them all in one go. Take your time and try to apply them in questions to learn them. Do a lot of locus problems. Again, lots of types, and solving many problems of different types will help you.

3. Vectors and 3D- 3D is just a continuation of 2D Geometry. Have a good thinking of the problem in 3D. It will help you. Again, formulae-remember them. You won't face much problem in 3D. Vectors would give you problems :p. Well, try to think of vectors in terms of 3D when in trouble. There are a few standard techniques(taking dot product, cross product with something, etc.) try to implement them and see if they help. Keep on solving a variety of problems. Various lines forms get confusing. Tricky questions can be easily formed in vectors. Try to think of all the formulae available to you. It will surely help. Again, this is mostly based on revising and practicing. 

So, Coordinate Geometry, Vectors and 3D are mostly calculation based, with a handful of central concepts which apply to all the problems and situations. If you study it deeply you would find beautiful connections between various formulae and situations. I'll leave them for you to discover(NCERT style :p).

BOOKS

As usual, if you go to a coaching, follow that book. If you don't you can take this book from Resonance. I can't find the link for other books, so you'll have to take the ones mentioned below(I was from Resonance and found their study material pretty good).

If you want more practice, go for Arihant coordinate geometry and Vectors and 3D.

S.L. Loney is another beautiful book, with some very good questions. It is surely worth solving, if you have time. Apart from this, A. Das Gupta has some really nice questions in 2D coordinate geometry. Do solve them if you want a very good grasp and rank.

So, do well in coordinate and Vectors and 3D. They carry a huge weightage. They need some revision and practice. Give your best, and let me know if you have any doubts by commenting below.

All the best!!!

Also see : Calculus, Algebra, Trigonometry, Best books for JEE