Let y(t) be a unit speed regular parametrized curve with nonzero curvature. Consider the surface patch o(t,0) = y(t) + (R cos 6) n(t) + (R sin 0) B(t) where R is a positive constant and n(t) and B(t) are respectively the principal normal and binormal vectors at y(t). (i) Find conditions on a and k(t) which guarantee that o is a regular surface patch. (ii) Compute the first fundamental form of the surface patch. (iii) Evaluate the area of the part of the surface patch where a

3. Let 7(t) be a unit speed regular parametrized curve with nonzero curvature. Consider the surface patch 0(t, c9) = 7(t) + (R cos 6) n(t) + (R sin 6) B(t) where R is a positive constant and n(t) and B(t) are respectively the principal normal and binormal vectors at 7(t). (i) Find conditions on a and [(t) which guarantee that a is a regular surface patch. (ii) Compute the rst fundamental form of the surface patch. (iii) Evaluate the area of the part of the surface patch Where a