Question

I have a question about my Engineering Math. lectures. I know there are a few solution of this question on Cheg but I couldn’t understand them so please solve it step by step and clearly. Many Thanks..        

Question= Think a very long (infinitely long) water pipeline, which is buried underground (inside earth). Consider the earth’s surface as xy plane, and +z direction is towards to inside of earth. With the aid of a ground penetrating radar (GPR), the coordinates of two different points on the underground pipeline are measured as P (20, 20, 30) and Q (0, 15, 40). Assume that there is a driller at the origin, which is able to drill ground (earth) in a straight path. For the minimum cost, the driller wants to reach the pipeline in a possible shortest distance. Model the water pipeline with an infinite line having zero thickness and take flat earth surface.

a) What is this shortest distance?

b) What are the coordinates of this nearest point?

c) By considering spherical coordinates, what should theta and phi angles in degrees be for the driller to reach the pipeline along the shortest path?

Answer 1