Hi, another vector question I'm afraid

I have the 4 lines:

, .

, .

I need to show that all 4 lines lie in a single plane and fine the Cartesian Equation of the plane.

The Cartesian equation of a plane is in the form , so from this I can set up the following equations:

From these I can get all in terms of .

,

Putting these values back into the original Cartesian Equation I got:

, which can be simplified to .

Is this correct so far or have I gone horribly wrong?

Thanks