What is the cross product a x b of the two vectors a = 64.00 m directed due east and b = 32.00 m directed 30° north of east?

the 32@30NofE has two components, N, and E

The E component has zero cross product with the due E, but the N component and due E component has a component. Curiously, you have a problem defining its direction. Due Ease X N means coming out of the page, if N is upward. On Earth, that is difficult, because the "page" is not flat, but depends on latitude.