For the following possibilities of vectors x, y, and z, in which cases does z lie between x and y, that is, in which cases do there exist numbers λx ≥ 0 and λy ≥ 0 such that z = λx x + λy y?
i) x = (3, 1), y = (-2, -1), and z = (4, 1),
ii) x = (1, 0, 0), y = (0, 1, 0), and z = (0, 0, 1),
iii) x = (5, 2), y = (-8, 4), and z = (15, 6).
Select one:
a. only i)
b. only ii) and iii)
c. only i) and ii)
d. only i) and iii)