I am not sure if this is the right place to ask, but many mathematicians are knowledgeable and interested also in history of math, so here I am.

I am curious to know when the right-hand-rule for vector product was established and used consistently.

I am reading an introductory algebraic geometry text by Victoria Scott from 1894. I have noticed that she seems to use a left hand rule for the computation of vector product: in order to compute an area of a triangle she does a product of the sides (that I assume is the vector product) but, with the order chosen, she should get a negative area. And when she wants a negative area (to remove from another area)… the result should be positive with the modern convention. Since at the end she is just interested in plane geometry, consistency of the signs is the only thing that she needs, and she gets it. But this has aroused my curiosity about the history of the right-hand-rule and the orientation of axes in the euclidean 3-space….