[defen]

In a geometric setting - if you have two vectors, you can position them so that both have one end at the origin. This spans a plane (test it out yourself in 2D or 3D space with two pencils, put the eraser at the origin for each; it's a parallelogram). The area of the plane will depend on the length of the pencils. You can assign an orientation to the plane by imagining a rotor embedded in the plane that spins either clockwise or counterclockwise.

[abainbridge]

Hmmm.

"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.

[defen]

Yes, when I said plane I really meant the parallelogram. By rotor I literally just meant "a thing that spins" - you could draw a circle on the parallelogram with an embedded arrow describing the direction it is spinning - that arrow could either be going clockwise or counterclockwise.

[klodolph]

The length of a line is infinite too. If you think of a vector as a line + magnitude, it's a bit more natural to think of a bivector as a plane + magnitude.