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Tangent Vector

Basic definition

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

Detailed definition

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.

Related terms

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

Educational grade level

college level

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