$\frac{x-0}{1}=\frac{y-0}{1}=\frac{z-0}{1}=\alpha $$\quad..............(1)$
$Q(\alpha, \alpha, 1)$
Direction ratio of $PQ$ are
$\lambda-\alpha, \lambda-\alpha, \lambda-1$
Since $PQ$ is perpendicular to $(1)$
$\therefore \quad \lambda-\alpha+\lambda-\alpha+0=0 $
$ \lambda=\alpha$
$\therefore \quad$ Direction ratio of $P Q$ are
$0,0, \lambda-1$
Another line is
$\frac{x-0}{-1}= \frac{y-0}{1}=\frac{z+1}{0}=\beta $
$\therefore \quad R(-\beta, \beta,-1) $
$\therefore \quad \text { Direction ratio of PR are } $
$ \lambda+\beta, \lambda-\beta, \lambda+1$
Since $P Q$ is perpendicular to $(ii)$
$\therefore -\lambda-\beta+\lambda-\beta=0 $
$ \beta=0 $
$\therefore \quad R(0,0,-1) $
$\text { and } \text { Direction ratio of } P Q \text { are } \lambda, \lambda, \lambda+1 $
$\text { Since } P Q \perp PR $
$\therefore 0+0+\lambda^2-1=0 \Rightarrow \lambda= \pm 1 \Rightarrow B, C$
For $\lambda=1$ the point is on the line so it will be rejected.
$\Rightarrow \quad \lambda=-1$
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