Unit Normal to a Plane Curve

The unit outwards normal to a curve in the

\[xy\]

plane can be derined in terms of the unit tangent vector

\[\mathbf{T}\]

to the curve taken counterclockwise and the unit vector

\[\mathbf{k}\]

along the

\[z\]

axis by considering a right angled cpprdinate system on the curve.

For the

\[\mathbf{n} \mathbf{T} \mathbf{k}\]

system above

\[\mathbf{k} \times \mathbf{T} = \mathbf{n}\]