(a) True. (b) False.
Work Step by Step
(a) True. For any two vectors $u=(u_1,u_2,...,u_n), v=(v_1,v_2,...,v_n)\in R^n$ are equal if and only if their coresponding components are equal, that is, $$u_1=v_1, ..., u_n=v_n.$$ (b) False. $-v$ is the additive inverse and this can be shown from the property of the additive inverse, $$v+(-v)=0.$$