2. define a relation on r3 by (ri, t2.3) no (ny, if and only if there exists ? 0 such that (ai, a2.xs) . a(y? , show that ~ is an equivalence relation (reflexive, symmetric, transitive). 3. let rp2 be the set of equivalence classes fordefined in the previous exercise. (rp2 is called the real projective plane.) for i = 1, 2, 3, set ui-flx] e rp2 : xì 0), where [x]-[x1,x2, x3] is the equivalence class for x define p ur2 by p1(1,2,(2/) similarly define 92 and p3 r2 byy1([a: 1, a2 , a's] (x2/x1,x3/m). similarly = (a) show that each pi is surjective, and find p (b) show that p1, p2, and p3 are 2-charts that make rp2 into a 2- manifold. (just do one transition function and argue that the others are analogous.)