Setting rotation of the 3d cursor along the surface

When we set the position and rotation of 3d cursor by clicking a surface there is one rotation parameter is missing. Which direction will be the z axis of 3d cursor?

We can set this with click and drag. The place we click sets the position. y axis will be same with the surface normal and the way we drug sets the roll.

Z axis of 3d cursor become important when you add new geometry aligned to a surface or set transform orientation to 3d cursor.