# Differential Geometry/Binormal Vector, Binormal Line, and Rectifying Plane

Consider a curve C of class of at least 2 with the arc length parametrization f(s).

The **unit binormal vector** is the cross product of the unit tangent vector and the unit principal normal vector,

which has a magnitude of 1 because t(s) and p(s) are orthogonal, and which are orthogonal to both t(s) and p(s).

The line passing through f(s) in the direction of b(s) is called the **binormal line**, and the plane spanned by the b(s) and t(s) is called the **rectifying plane.**

Now we have equations of the three planes. The normal plane is given by the equation , the rectifying plane is given by the equation , and the osculating plane is given by the equation . It is easy to see that the earlier formula for the osculating plane is the same as this formula.