Three lines are given by
$$\overrightarrow{r} = \lambda \widehat{i}, \lambda \in R$$
$$\overrightarrow{r} = \mu (\widehat{i} + \widehat{j}), \mu \in R$$ and
$$\overrightarrow{r} = v (\widehat{i} + \widehat{j} + \widehat{k} ), v \in R$$.
Let the lines cut the plane x + y + z = 1 at the points A, B and C respectively. If the area of the triangle ABC is $$\triangle$$ then the value of $$(6\triangle)^2$$ equals__________ .