Find a vector parallel to the intersection of the planes and .

As i am in a bit of a pinch regarding time for development. I was wondering if anyone has developed (and is prepared to share with me) questions relating to the general vector form of;

equations for a lines in 2d of the form (please excuse the TeX)

\bm{l} = \vec{OA} + \lambda \vec{AB}

such as

\bm{l} = <2,-1> + \lambda <2,4>

and planes in 3d

\bm{p} = \vec{OA} + \lambda \vec{AB} + \mu \vec{AC}

such as

\bm{p} = <4,2,0> + \lambda <-1,-1,1> + \mu <0,-3,1>