Vectors in Space · Challenge problem

Let $\mathbf a = (1, 1, 1)$. The vector $\mathbf x$ satisfies both $\mathbf x \times \mathbf a = (1, -2, 1)$ and $\mathbf x \cdot \mathbf a = 6$. Find $\lVert \mathbf x \rVert^2$.