please solve C

Question 2. In this question, you will prove the following statement step by step. "Let be the Euclidean (2) norm. For all x,yRn, we have xyxy. Moreover, the equality holds if and only if x=ky for some kR." The inequality given by (1) is called the Cauchy-Schwarz inequality. a) Show the statement for x=0Rn. For the remaining parts, assume that x=0. b) Show that the following equality holds for all x,yRn,x=0 : x21x2y(xy)x2=x2y2xy2 c) Using equality (2), show that inequality (1) holds