There is an error in the line's description, any normal of a line is perpendicular to the line itself (all through a point of the line are contained in a plane

There is an error in the line's description, any normal of a line is perpendicular to the line itself (all through a point of the line are contained in a plane perpendicular to the line, with two special ones, the principal normal and the binormal, as with every curve) and does not point "in the direction of the line". A remark: a plane has two (different) unit length normals, which point in exactly opposite directions (one can be obtained by multiplying the other by -1). This determines the positive and negative half-spaces in which each plane splits the 3 dimensional space - the positive and negative direction, which appears for example in the distance calculation on the site.