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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?

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    Я б сказал проекция к нормали k и честно говоря ничего другого в данном контексте не слышал.
    – shabunc
    Dec 28, 2020 at 22:52
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    I reject the idea of using “rejection” like that in math in English. Please do not try to create a Russian analogue of that ridiculous terminology. Follow the suggestion of shabunc.
    – KCd
    Dec 29, 2020 at 2:41
  • I have never heard vector rejection used in mathematics. Jan 1, 2021 at 14:52
  • @shabunc isn't it проекция на нормаль к оси k?
    – il--ya
    Dec 15, 2021 at 9:47
  • @il--ya yeah, it definitely might be, may be my memory does not serve me well
    – shabunc
    Dec 27, 2021 at 20:51

2 Answers 2

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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.

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It can be translated as "вертикальная компонента вектора v", but only in the context of projection.

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