Three lines 
 $L_1:\overrightarrow{r}=\lambda \widehat{i},\lambda \in ℝ$
 $L_2:\overrightarrow{r}=\widehat{k}+\mu \widehat{j}.\mu \in ℝ$
 $L_3:\overrightarrow{r}=\widehat{i}+\widehat{j}+v\widehat{k}.v\in ℝ$
are given . For which point(s) Q on L₂ can we find a point P on L₁ and a point R  on L₃ so that  P,Q and R are colliner ?
 

P.V of point P, $\overrightarrow{p}=\lambda \widehat{k}$
       P.V. of point Q, $\overrightarrow{q}=\mu \widehat{j}+\widehat{k}$
      P.V. of point R,  $\overrightarrow{r}=\widehat{i}+\widehat{j}+r\widehat{k}$ 
      PQR  are collinear , Hence  $x\left(\overrightarrow{PQ}\right)=y\left(\overrightarrow{PR}\right)$
      $\Rightarrow \frac{x}{y}=\frac{1-\lambda }{-\lambda }=\frac{1}{\mu }=r$
$\Rightarrow \overrightarrow{q}=\frac{1}{r}\widehat{j}+\widehat{k}$  or $\overrightarrow{q}=\frac{\lambda }{\lambda -1}\widehat{j}+\widehat{k}$ , where  $r\ne 0,\lambda \ne 0,\frac{\lambda }{\lambda -1}\ne 1$
 $\Rightarrow \mu \ne 0,1$