Direction cosines of the tangent principal normal and binormal

Definition:(1.)Principal Normal:The normal lying in the osculating plane at a point p of a given space curve is called the principal normal to the curve at the point p.

(2.)Binormal:The normal perpendicular to the principal normal of a given curve at a point p is called binormal of the curve at that point.

Direction cosines of the tangent,principal normal and binormal

(3.)Angles between tangent and the given line,Angles between binormal and the given line 

Direction cosines of the tangent,principal normal and binormal

(4.)The condition of the three directions are coplanar

Direction cosines of the tangent,principal normal and binormal