If the line $\frac{x-4}{1}=\frac{y-2}{1}=\frac{z-q}{p}$ lies completely in the plane $2x-4y+z=7,$ then the ordered pair $\left(p,q\right)$ is

Since the line lie in the plane, so $\left(\mathrm{4,2},q\right)$ also lie in the plane and vector along the line is perpendicular to normal to the plane

Therefore, $2-4+p=0\Rightarrow p=2$ and $8-8+q=7\Rightarrow q=7$

Hence, the ordered pair is $\left(2,7\right)$