"The area of the plane will depend on the length of the pencils". Surely the area of the plane is infinite? The area of the _parallelogram_ will depend on the length of the pencils.

And I can't see how "you can assign an orientation to the plane" other than by changing the directions of the pencils. Again this description sounds like it refers to the parallelogram, not the plane.

And I don't know what a rotor is.

But other than that, I'm doing great.