If $$\lambda_1 < \lambda_2$$ are two values of $$\lambda$$ such that the angle between the planes $$P_1: \vec{r} \cdot (3\hat{i} - 5\hat{j} + \hat{k}) = 7$$ and $$P_2: \vec{r} \cdot (\lambda\hat{i} + \hat{j} - 3\hat{k}) = 9$$ is $$\sin^{-1}\frac{2\sqrt{6}}{5}$$, then the square of the length of perpendicular from the point $$(38\lambda_1, 10\lambda_2, 2)$$ to the plane $$P_1$$ is