3 ms·
> the "dot product" and "cross product" are not necessarily as "natural" as you may have been lead to believe The cross product, sure: its problem is that it d
by creata 3y ago
> the "dot product" and "cross product" are not necessarily as "natural" as you may have been lead to believe
The cross product, sure: its problem is that it dualizes unnecessarily, making you deal with a normal vector when you almost always just want the plane.
But what did the dot product ever do to you?
- npsomaratna 3y agoBut don't you need the normal vector to define the plane? (Genuine question)
- alok-g 3y agoA bivector is just as good for the purpose. Think of it as a generalization of a directional arrow (vector) into an oriented area (bivector). The OP talk shows good visualizations if you haven't watched yet.
- npsomaratna 3y agoGot it, thank you. (And facepalm, this is something I should have remembered!)
- tobinfricke 3y agoA plane does not have a unique "normal vector" in higher than 3 dimensions.
- npsomaratna 3y agoGood point, thank you.
- tobinfricke 3y ago> But what did the dot product ever do to you? Fair enough. What I was getting at is that "standard vector analysis" is a choice, and it turns out that there are alternatives where things are defined differently.