If two lines L_1 and L_2 in space, are defined by L_1={x=√ λ y+(√ λ -1), z=(√ λ -1) y+√ λ } and L_2={x=√ μ y+(1-√ μ ), z=(1-√ μ ) y+√ μ }, then L_1…

If two lines $\displaystyle \mathrm{L}_1$ and $\displaystyle \mathrm{L}_2$ in space, are defined by $$\begin{aligned} & \mathrm{L}_1=\{x=\sqrt{\lambda} y+(\sqrt{\lambda}-1), \\ & z=(\sqrt{\lambda}-1) y+\sqrt{\lambda}\} \text { and } \\ & \mathrm{L}_2=\{x=\sqrt{\mu} y+(1-\sqrt{\mu}), \\ & z=(1-\sqrt{\mu}) y+\sqrt{\mu}\}, \end{aligned} $$ then $\displaystyle \mathrm{L}_1$ is perpendicular to $\displaystyle \mathrm{L}_2$, for all non-negative reals $\displaystyle \lambda$ and $\displaystyle \mu$, such that :