question_answer

If two lines  \[{{L}_{1}}\] and  \[{{L}_{2}}\] in space are defined by\[{{L}_{1}}=\left\{ x=\sqrt{\lambda }y+(\sqrt{\lambda }-1),\,z=(\sqrt{\lambda }-1)y+\sqrt{\lambda } \right\}\]   and \[{{L}_{2}}=\left\{ x=\sqrt{\mu }y+(1-\sqrt{\mu }),\,z=(1-\sqrt{\mu })y+\sqrt{\mu } \right\}\]then \[{{L}_{1}}\] is perpendicular to \[{{L}_{2}}\] for all non-negative reals \[\lambda \] and \[\mu \], such that

A)  \[\lambda =\mu \]                                        

B)  \[\lambda +\mu =0\]

C)  \[\lambda \ne \mu \]                                   

D)  \[\sqrt{\lambda }+\sqrt{\mu }=1\]