$\mathbb{R}^3$ \ $\mathbb{Q}^3$ is a union of disjoint lines, The lines are not in an axis direction.

Question

I have a folowing question:

$\mathbb{R}^3$ \ $\mathbb{Q}^3$ is a union of disjoint lines. This exercise is in the book: Set theory for the working mathematician of Krzysztof Ciesielski.

Any can give help me in how make a selection of the disjoint lines?

Thanks.