Equation of line passing through $P(7,10,11)$ along the line $\frac{x-9}{2}=\frac{y-13}{3}=\frac{z-17}{6}$ is

$$\frac{x-7}{2}=\frac{y-10}{3}=\frac{z-11}{6}=\lambda$$

Let the point on the line is

$$Q(2 \lambda+7,3 \lambda+10,6 \lambda+11)$$

$Q$ lies on line $\frac{x-4}{1}=\frac{y-4}{0}=\frac{z-2}{3}$

$$\begin{aligned} & 3 \lambda+10=4 \Rightarrow \lambda=-2 \\ & \therefore \quad Q(3,4,-1) \\ & P Q=\sqrt{16+36+144}=14 \end{aligned}$$