From Wikipedia:
Using the dot and cross products, the vector v can be decomposed into components parallel and perpendicular to the axis k, where the component parallel to k is called the vector projection of v on k, and the component perpendicular to k is called the vector rejection of v from k.
"Vector projection" is проекция вектора v на k in Russian, but I've never heard the term "vector rejection" before — in English or in Russian.
Is there an established Russian term for it?
If you need a term, you can say ортогональная составляющая вектора v относительно оси k (as opposed to ортогональная проекция вектора v на ось k). Bear in mind, though, that this is not a term from vector algebra, which seems to be the context of your question; this is a term from abstract algebra.
Other than that, the best way to describe this concept would be проекция вектора v на плоскость, перпендикулярную оси k.
It can be translated as "вертикальная компонента вектора v", but only in the context of projection.
