The largest value of $$𝑎$$, for which the perpendicular distance of the plane containing the lines $$\vec{r} = \hat{i} + \hat{j} + \lambda \hat{i} + a \hat{j} - \hat{k} \quad \text{and} \quad \vec{r} = \hat{i} + \hat{j} + \mu \hat{i} + \hat{j} - a \hat{k}$$ from the point 2, 1, 4 is $$\sqrt{3}$$, is