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The special theory of relativity describes the motion and dynamics of objects moving at significant fractions of the speed of light.

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Can a component of velocity be greater than the speed of light?

No, because the total magnitude of the speed vector may not exceed the speed of light, and it is itself greater than the absolute value any of its component : $$\vec{v}=$\begin{bmatrix}x\\y\\z\end{bm …
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