If two lines $L _ { 1 }$ and $L _ { 2 }$ in space, are defined by
$$\begin{gathered} L _ { 1 } = \{ x = \sqrt { \lambda } y + ( \sqrt { \lambda } - 1 ) , \\ z = ( \sqrt { \lambda } - 1 ) y + \sqrt { \lambda } \} \text { and } \\ L _ { 2 } = \{ x = \sqrt { \mu } y + ( 1 - \sqrt { \mu } ) , \\ z = ( 1 - \sqrt { \mu } ) y + \sqrt { \mu } \} \end{gathered}$$
then $L _ { 1 }$ is perpendicular to $L _ { 2 }$, for all nonnegative reals $\lambda$ and $\mu$, such that :
(1) $\sqrt { \lambda } + \sqrt { \mu } = 1$
(2) $\lambda \neq \mu$
(3) $\lambda + \mu = 0$
(4) $\lambda = \mu$