In the beautiful town of Darjeeling in the Himalayan foothills, the city planning committee wants…

In the beautiful town of Darjeeling in the Himalayan foothills, the city planning committee wants to construct two major roads to connect the various neighbourhoods. The two roads are represented by the equations $\frac{x+1}{3} = \frac{y+3}{5} = \frac{z+5}{7}$ and $\frac{x-2}{1} = \frac{y-4}{k} = \frac{z-6}{7}$. As an in charge of the planning committee, ensure that these roads lie on the same plane to facilitate efficient urban planning and infrastructure development.