The intersection part of a plane I have a cube sliced by a plane:

I would like to get the part of the plane inside the cube. So I figured a boolean modifier would the trick. Whether I apply it to the cube or plane or chose union, intersect or difference I always end up with some 3D object - some part of the cube. I would like to have only the plane part of the boolean.
Following @Gordon Brinkmann's comment, in Blender 2.9x, using the 'Fast' Boolean option, (the modifier assigned to the plane,) it seems to work OK, here:

...across the angles.

But 'Exact' seems to fail; it includes the volume in the cube behind the plane's normal.