For a more general — but much more technical — treatment of tangent vectors, see tangent space.In mathematics, 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. Formally, a tangent vector at the point
x
{\displaystyle x}
is a linear derivation of the algebra defined by the set of germs at