Line L_1 passes through the point (1,2,3) and is parallel to z -axis. Line L_2 passes through the point (λ, 5,6) and is parallel to y -axis. Let for…

Line $\displaystyle \mathrm{L}_1$ passes through the point $\displaystyle (1,2,3)$ and is parallel to $\displaystyle z$-axis. Line $\displaystyle \mathrm{L}_2$ passes through the point $\displaystyle (\lambda, 5,6)$ and is parallel to $\displaystyle y$-axis. Let for $\displaystyle \lambda=\lambda_1, \lambda_2, \lambda_2<\lambda_1$, the shortest distance between the two lines be $\displaystyle 3$ . Then the square of the distance of the point $\displaystyle \left(\lambda_1, \lambda_2, 7\right)$ from the line $\displaystyle \mathrm{L}_1$ is