Inverse vector

An inverse rectilinear vector ^[1] $ā$ ' is a vector which is co-directed (in the same direction as) a vector $ā$ and differs from it in magnitude according to: $|$ $ā$ ' $| = \frac{1}{| ā |}$
Projections on the coordinate axes of inverse rectilinear vectors are equal according to: $a'_{x} = \frac{a_{x}}{a_{x}^{2} + a_{y}^{2} + a_{z}^{2}}; a'_{y} = \frac{a_{y}}{a_{x}^{2} + a_{y}^{2} + a_{z}^{2}} a'_{z} = \frac{a_{z}}{a_{x}^{2} + a_{y}^{2} + a_{z}^{2}}$

An inverse angular vector $ȃ$ ' is similarly a vector which is co-directed with a vector $ȃ$ and differs from it in magnitude: $|$ $ȃ$ ' $| = \frac{1}{| ȃ |}$
Projections on the coordinate planes of inverse angular vector are equal according to: $a'_{x y} = \frac{a_{x y}}{a_{x y}^{2} + a_{y z}^{2} + a_{z x}^{2}}; a'_{y z} = \frac{a_{y z}}{a_{x y}^{2} + a_{y z}^{2} + a_{z x}^{2}} a'_{z x} = \frac{a_{z x}}{a_{x y}^{2} + a_{y z}^{2} + a_{z x}^{2}}$

Inverse vectors are used in mathematics to perform vector division operations.

References

↑ Kharchenko,Y.M.(2017). Angular vectors in the theory of vectors. Journal of Mathematics Research vol.9 no.5 p.71

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[1] Kharchenko,Y.M.(2017). Angular vectors in the theory of vectors. Journal of Mathematics Research vol.9 no.5 p.71

[1]

Inverse vector

References

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