Well, you don't mean "plane". A plane has no "corners" but extends infinitely. You mean some rectangle in a plane. In order that your explanation of "dip direction" and "dip" make sense, I think we have to assume that the "dip direction" is measure, parallel to the xy-plane, clockwise from the positive x direction. If that is the case then, with "dip direction" , a normal vector to this plane will have x and y components and , respectively. The "dip" then is below the xy-plane so if the "dip" is angle then the z component of the normal vector will be . That is, a normal vector is of the form and so the equation of the plane is .

You say that "fracture height and length", measure "how far the plane extends in each direction" but you do not say what those directions are. Is one the "dip direction" and the other perpendicular to it?