If λ_1<λ_2 are two values of λ such that the angle between the planes P_1: r (3 i -5 j + k )=7 and P_2: r ·(λ i + j -3 k )=9 is sin^-1((2 √ 6)/5),…

If $\displaystyle \lambda_1<\lambda_2$ are two values of $\displaystyle \lambda$ such that the angle between the planes $\displaystyle \mathrm{P}_1: \overrightarrow{\mathrm{r}}(3 \hat{i}-5 \hat{j}+\hat{k})=7$ and $\displaystyle \mathrm{P}_2: \overrightarrow{\mathrm{r}} \cdot(\lambda \hat{i}+\hat{j}-3 \hat{k})=9$ is $\displaystyle \sin ^{-1}\left(\frac{2 \sqrt{6}}{5}\right)$, then the square of the length of perpendicular from the point $\displaystyle \left(38 \lambda_1, 10 \lambda_2, 2\right)$ to the plane $\displaystyle \mathrm{P}_1$ is $\displaystyle \_\_\_\_$.