I get a vector by producing two unit vectors. I add them up as cosines and sines.

v3.x = v1.x * v2.x - v1.y * v2.y v3.y = v1.y * v2.x + v1.x * v2.y

Does this operation have a name in the context of vectors?

    2 answers 2

    Complex multiplication looks like this.

     (a + ib)(c + id) = (ac - bd) + i(bc + ad) ...где i - мнимая единица, для которой i^2 = -1

    ... which in a geometric model for vectors (on the complex plane) of unit length gives another vector of unit length, whose argument (angle with Re +, horizontal axis "to the right") is the sum of the arguments of the components.

    If they were not single, the length of the result would be the product of their lengths.

      I suspect that there is no name, because asymmetric operation - for X you consider the difference of squares (it looks like a scalar product, only the sign is not the same), and for Y - the cross product (and again the sign is not the same).

      I wonder how you came to this formula and how to use the results of its calculation? Maybe these are 2 unrelated parameters and the signs are not the ones - then this is just a scalar and vector product.

      • It is symmetric (on real numbers anyway). The difference involves the works of different components of the vectors. If you swap vectors, only the order in the works is changed, but not the result. - D-side
      • @ D-side confuses me that it is not symmetrical about x / y. In any case, I would like to get clarification from the author of the question - maybe they will shed light on the term that is needed. - Kromster
      • Well, that's just fine. The numerical representation of a vector on a plane is an ordered pair of numbers. Yes, better wait for the TCA. - D-side