My son, studying something equivalent to highschool, has to do a work about some topic in mathematics. The topic has to be some important and "fruitful" theorem (why is important, who stated it, who used it, what are the far reaching consequences...) I think is not far from the idea to choose this operation, the dot product, as it maintains the point about the fruitful thing (I have not to explain the central rôle it has in elemental analitic geometry and in general all derived from its more abstact definition in algebraic structures)
But my question is about the origin or history of this useful tool, e.g. who put it into the vector spaces, what and when we can consider as the first use of it. Of course, any ideas not related to the history part will be welcome too.
Added
It'd be interesting too to know who extended this concept to other areas and when.
Thanks in advance.