Im a bit stuck here, any help will be appreciated, thanks..
Find the equation of the plane containing two parallel lines which are: r=a+(alpha)u and r=b+(beta)u
Assuming that these are indeed two lines then the normal to the planes is $\displaystyle \vec{N}=\vec{ab}\times \vec{u}$.
Let $\displaystyle \vec{R}=<x,y,z>-\vec{a}$ so the plane is $\displaystyle \vec{N}\cdot\vec{R}=0.$