I know c) is not necessarily true. And I think if d) were true then $\displaystyle (u \times v) \cdot (u \times w) \neq 0 $

But aren't a) and b) both true? a) follows from the definition of orthogonal planes because of perpendicular normals, and I can't think of a counterexample for b); somehow though, my thinking is flawed because the question is multiple choice.