## 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
$\mathbf{k} \times \mathbf{T} = \mathbf{n}$