Tangent vector

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For a more general, but much more technical, treatment of tangent vectors, see tangent space.

A tangent vector is a vector that is tangent to a curve or surface at a given point.

Tangent vectors are described in the differential geometry of curves in the context of curves in Rn. More generally, tangent vectors are elements of a tangent space of a differentiable manifold.

Tangent vectors can also be described in terms of germs. In other words, a tangent vector at the point x is a linear derivation of the algebra defined by the set of germs at x