Finding the Curvature of a Line

Show that the curvature of a line is \(0\).

Solution For a line, the unit tangent vector \(\mathbf{T}\) is along the constant direction of the line, so \(\mathbf{T}\) is a constant and \(\dfrac{d\mathbf{T}}{ds}=\mathbf{0}\). The curvature \(\kappa\;=\;\left\Vert \dfrac{d\mathbf{T}}{ds}\right\Vert\) of a line is \(0\).