切矢量是一个沿着曲线或曲面在给定点的方向：

• 曲线的微分几何，描述了 R 中的曲线的切矢量；
• 切空间，流形理论中的一般概念。

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 R. 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 is a linear derivation of the algebra defined by the set of germs at .