Solution: Let $\theta$ be the angle between any pair of vectors. Since $\mathbfu \cdot \mathbfv = \cos\theta = \frac12$, $\theta = 60^\circ$. The magnitude squared is $|\mathbfu + \mathbfv + \mathbfw|^2 = 3 + 2(\mathbfu \cdot \mathbfv + \mathbfu \cdot \mathbfw + \mathbfv \cdot \mathbfw) = 3 + 2(3 \cdot \frac12) = 3 + 3 = 6$. Thus, the maximum value is $\sqrt6$. - Crosslake