Assignment:
Suppose a twisted curve is defined in terms of the arclength s by
r(s)=sech?(θ) cos?(s)i+sech?(θ) sin?(s)j+s tanh?(θ)k,
where θ is a constant parameter.
Determine
(i) the tangent t(s),
(ii) the normal n(s),
(iii) the binormal b(s),
(iv) the curvature κ,
(v) the torsion τ.
Provide complete and step by step solution for the question and show calculations and use formulas.