I am thinking about a such operation. Which it need to have:
- It needs to be $\mathbb{R}^n\times{\mathbb{R}^n}\rightarrow\mathbb{R}^n$
- The result needs to be perpendicular to the arguments (thus, scalar product need to be zero)
- It needs to be unambiguous.
Does a such operation existing? If not, how were it possible to fill at least 2 of these 3?