Past exam of the mathematics course of the University of Cambridge / 2024 / ib / Paper 1 / 11E / ii / Solution

Tangency along $\gamma$ meansfor every $t$. Consequently $\ddot{\gamma }(t)$ is perpendicular to the first tangent plane exactly when it is perpendicular to the second. The ambient characterization of a geodesic therefore proves the tangency invariance of an ambient-surface geodesic: