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# If two lines L_1 and L_{2 in space, are defined by

Question:

If two lines $L_{1}$ and $L_{2}$ in space, are defined by

$\mathrm{L}_{1}=\{\mathrm{x}=\sqrt{\lambda} \mathrm{y}+(\sqrt{\lambda}-1)$

$\mathrm{z}=(\sqrt{\lambda}-1) \mathrm{y}+\sqrt{\lambda}\}$ and

$\mathrm{L}_{2}=\{\mathrm{x}=\sqrt{\mu} \mathrm{y}+(1-\sqrt{\mu})$

$z=(1-\sqrt{\mu}) y+\sqrt{\mu}\}$

then $L_{1}$ is perpendicular to $L$, for all non-negative reals $\lambda$ and $\mu$, such that :

1. $\lambda=\mu$

2. $\lambda \neq \mu$

3. $\sqrt{\lambda}+\sqrt{\mu}=1$

4. $\lambda+\mu=0$

Correct Option: 1, 4

Solution: