Equation of line through point $(-1,2,1)$ is $\rightarrow$

$$\begin{aligned} &\Rightarrow \frac{x+1}{2}=\frac{y-2}{3}=\frac{z-1}{4}-(2)=\lambda\\ &\text { So, }\left[\begin{array}{l} x=2 \lambda-1 \\ y=3 \lambda+2 \\ z=4 \lambda+1 \end{array}\right. \end{aligned}$$

By $(1) \rightarrow \frac{x+2}{3}=\frac{y-3}{2}=\frac{z-4}{1}=\mu($ Let $)$

So, $\left[\begin{array}{l}x=3 \mu-2 \\ y=2 \mu+3 \\ z=\mu+4\end{array}\right.$

For intersection point 'P'

$$\begin{aligned} & \mathrm{x}=2 \lambda-1=3 \mu-2 \\ & \mathrm{y}=3 \lambda+2=2 \mu+3 \quad\left[\begin{array}{l} \lambda=1 \\ \mu=1 \end{array}\right] \\ & \mathrm{z}=4 \lambda+1=\mu+4 \\ & \text { So, point } \mathrm{P}(\mathrm{x}, \mathrm{y}, \mathrm{z})=(1,5,5) \\ & \& \mathrm{Q}(4,-5,1) \\ & \therefore \mathrm{PQ}=\sqrt{9+100+16} \\ & =\sqrt{125}=5 \sqrt{5} \end{aligned}$$