A mathematical representation of a plane can be defined in two ways (or more, but these are the ones I often use). You can either use three vector points or a vector point paired with a vector normal.
Three vector points define the “surface” of a plane by actually representing the a polygon of a plane. Direction of the plane can be defined by figuring out if the vectors are clock wise or anti clockwise. If you look at the image above, it would be the vectors a, b and c.
The other method which is more common as it requires fewer vectors. It requires a point somewhere on the plane and the normal which is the direction at which the plane is facing. If you look at the image above, it would be vector a or b or c and the plane normal would be the purple line.
Just remember that a plane in mathematical terms represents an infinite surface.
I’m not 100% sure what you’re trying to do however. Are you trying to find the intersection point between a ray and the surface?