Let V denote the set of ordered triples (x, y, z) and define addition in V as in R 3 . For each of the following definitions of scalar multiplication, decide whether V is a vector space. (i) a(x, y, z) = (ax, y, az) (ii) a(x, y, z) = (ax, 0, az) (iii) a(x, y, z) = (0, 0, 0) (iv) a(x, y, z) = (2ax, 2ay, 2az)