MathProblemsBank

7.5 Differential geometry

Problem: Find the unit vectors of the tangent, principal normal, and binormal of the curve. Compose the equations of the contiguous plane, the normal plane, the rectifiable plane at the point \( M_{0} \). \[ x=\cos ^{3} t, \quad y=\sin ^{3} t, \quad z=\cos 2 t . \]