Developing equation for specific wave

[infraray]

First off I apologize if this is in the wrong section, but I was not certain to where it belonged. If I am given a set of requirements for an e-m wave, i.e.: must contain all following: transverse, 3d, plane wave, propagation vector parallel to (-1,0,1), through plane defined by (1,0,1) and (0,1,0), etc (from memory). How would I begin to write an equation for this? I assuming I must start with say: Ae^ik[(alpha(x)+beta(y)+gamma(z))±wt] or some variant, but I am a bit weak when it comes to crafting equations. Perhaps I am lacking in my pedagogy, I just can't seem to see the big picture. Any help or recommendations would be greatly appreciated.

[Tide]

Your wave will have the form
\vec E = \vec E_0 e^{i \left( \vec k \cdot \vec x - \omega t \right)}
where \vec k is in the direction of propagation and \vec E _0 is perpendicular to \vec k and in the direction of polarization.