Mathematics - Vector Question with Solution | TestHub

Line $L_1$ passes through the point $(1,2,3)$ and is parallel to Z -axis. Line ${\mathrm{L}}_2$ passes through the point $(\lambda ,5,6)$ and is parallel to $y$-axis. Let for $\lambda ={\lambda }_1,{\lambda }_2,{\lambda }_2<{\lambda }_1$, the shortest distance between the two lines be 3 . Then the square of the distance of the point $\left({\lambda }_1,{\lambda }_2,7\right)$ from the line ${\mathrm{L}}_1$ is