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Decomposition of vectors, (in one of the x, y, z directions)

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When the magnitude of the vector is V and the direction is given as (x, y, z), the magnitude of the vector decomposed in each axis direction is as follows.

Vx = V*x/(x^2+y^2+z^2)^(1/2)

Vy = V*y/(x^2+y^2+z^2)^(1/2)

Vz = V*z/(x^2+y^2+z^2)^(1/2)

The above equations can be expressed in one equation as follows.

Vt = V*t/(x^2+y^2+z^2)^(1/2)

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Vt = V*t/(x^2+y^2+z^2)^(1/2)
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