There is an excellent series of YouTube videos about vectors and matrices here:

https://www.youtube.com/playlist?list=PLZHQObOWTQDPD3MizzM2xVFitgF8hE_ab

I've watched only #6 and #10, so far. The perspective is about areas and volumes of linear transformations.

#10 is about Cross Product, in 2D and 3D. A negative determinate means that the 3rd vector of the cross product is in the negative direction.
So maybe the vector.js code for Cross Product, line 287, should take the determinant (3D?), and then the code in line 34 modified so that in the case of a negative
determinant, bPt1 would be modified to be (0, 0, -1), instead of (0, 0, +1). (?)

Then the third vector "c" would still follow the right hand rule.
(Note that point "c" is calculated correctly, it is just the vector display that is not correctly oriented for the case of a negative determinant.)

In Pilou's example, when the order of the Cross Product is reversed, the sign of the determinant is reversed. The displayed vector should be negated.

- Brian