I'm having difficulty seeing how under the arc-length parameterization the equation of the tangent line $$\frac{X-x}{dx}=\frac{Y-y}{dy}=\frac{ Z-z}{dz}=u$$ can be written as $$\frac{X-x}{x'}=\frac{Y-y}{y'}=\frac{ Z-z}{z'},$$ where $x'=dx/ds,\, y'=dy/ds, \, z'=dz/ds.$ I'd also like to know what happens to the parameter $u$ at the end? Thanks for your help.
Update: The main question I was asking has been resolved for me now. I'd still like to know the answer to the second question relating to the parameter $u$.
