If $\frac{x-4}{1}=\frac{y-2}{1}=\frac{z-k}{2}$ lies in the plane 2x - 4y + z = 7 then the value of k is

As the line $\frac{x-4}{1}=\frac{y-2}{1}=\frac{z-k}{2}$ lies in the plane 2x - 4y + z=7 , 

the point (4,2,k) through which it passes must also lie on the given plane, 

and hence $2\times 4-4\times 2+\mathrm{k}=7 \mathrm{or} \mathrm{k}=7$