7.14 Differential geometry

Problem: For the curve given parametrically, find: 1. The vectors of the accompanying trihedron at the point \( t=t_{0} \); 2. The planes and lines of the accompanying trihedron at the point \( t=t_{0} \) 3. The tangent lines parallel to coordinate planes; 4. The contiguous planes perpendicular to the coordinate axes; 5. The curvature and torsion of the curve at the point \( t=t_{0} \). \[ \left\{\begin{array}{c} x(t)=2 t^{3} \\ y(t)=3 t \quad t_{0}=1 . \\ z(t)=3 t^{2} \end{array}\right. \]