# Calculus of Variations: Shortest distance between two points in 3D space

 P: 3,014 Minimize the functional: $$L[x(t), y(t), z(t)] = \int_{t_{0}}^{t_{1}}{\sqrt{\dot{x}^{2} + \dot{y}^{2} + \dot{z}^{2}} \, dt}$$ What are the Euler equations for each of the functions $x(t), y(t), z(t)$?