Rectifying plane

The plane of the Frénet frame (cf. Frénet trihedron) of a given point $ A $ on a curve $ \mathbf r = \mathbf r ( t) $( cf. Line (curve)) which is spanned by the tangent (cf. Tangent line) $ \mathbf t $ and the binormal $ \mathbf b $ to the curve at this point. The equation of the rectifying plane can be written in the form

$$ \left | or $$ ( \mathbf R - \mathbf r ) \mathbf r ^ \prime [ \mathbf r ^ \prime , \mathbf r

^ {\prime\prime} ]  =  0,

$$

where $ \mathbf r ( t) = \mathbf r ( x( t), y( t), z( t)) $ is the equation of the curve.

References

[a1]	M. Spivak, "A comprehensive introduction to differential geometry" , 2 , Publish or Perish (1970) pp. 1–5