Vectors in Space · Superchallenge problem

Let $\mathbf a = (1, 1, 0)$ and $\mathbf b = (2, -2, 3)$. Among all vectors $\mathbf x$ with $\mathbf a \times \mathbf x = \mathbf b$, find the smallest possible length $\lVert \mathbf x \rVert$.