A tangent vector is a vector pointing in the direction of the tangent line to the graph of a function.

For a curve with radius vector r(t), the unit tangent vector T^^(t) is defined by T^^(t) | congruent | (r^.)/( left bracketing bar r^. right bracketing bar ) | = | (r^.)/(s^.) | = | (d r)/(d s), where t is a parameterization variable, s is the arc length, and an overdot denotes a derivative with respect to t, x^. = d x/d t.

binormal vector | curvature | manifold tangent vector | normal vector | tangent | tangent bundle | tangent plane | tangent space | torsion

college level