Shortest Line in 3D Prove that the shortest path between two points in5.three dimensions is a straight line.Hint: Write the path in the parametric form x = x(u), yuse the Euler-Lagrange equations.y(u), and z =2(u). Then

The distance between the two points in the three dimensions can be given as follow:

Answered: Shortest Line in 3D Prove that the…

Classical Dynamics of Particles and Systems

5th Edition

ISBN:9780534408961

Author:Stephen T. Thornton, Jerry B. Marion

Publisher:Stephen T. Thornton, Jerry B. Marion

Chapter6: Some Methods In The Calculus Of Variations

Section: Chapter Questions

Problem 6.15P

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Shortest Line in 3D Prove that the shortest path between two points in 5. three dimensions is a straight line. Hint: Write the path in the parametric form x = x(u), y use the Euler-Lagrange equations. y(u), and z = 2(u). Then