So you object to the terms 'dot' and 'cross' product? They signify nothing beyond the notation itself.

Also, I use 'bool' everywhere in various langauges to denote a value that is 'true or false'. Should we change all usages of it to 'bit' or 'flag' or 'TwoValues'? It's an operator in all respects, and calling it 'bool' creates no confusion.