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

${\displaystyle b(s)=t(s)\times p(s)}$
Now we have equations of the three planes. The normal plane is given by the equation ${\displaystyle (x_{1}-f(s))\cdot t(s)=0}$, the rectifying plane is given by the equation ${\displaystyle (x_{1}-f(s))\cdot p(s)=0}$, and the osculating plane is given by the equation ${\displaystyle (x_{1}-f(s))\cdot b(s)=0}$. It is easy to see that the earlier formula for the osculating plane is the same as this formula.