part 1 b c and d, please!

1. (40 points) Define the set R.P" of 1-dimensional lines L passing through the origin in Rx+1 Equivalently, define an element L E R.P" as an equivalence class L = (y #0ERntly with y way for all a * 0 ER of (non-zero) vectors in Ra+ under scaling by (non-zero) real numbers. a. Write y = (yo, . .. ,y"). For each 0 x1(0kno1); and calculate xox, ($) explicitly as a map from (an open region of ) R." to R.". On what set of vectors & E R." is this mapping defined? Check that this mapping is smooth everywhere it is defined. e. Use the results above to demonstrate that RP" is an n-dimensional manifold