Question

A vector can be used to represent the path of a drill tip used to bore a deep mine shaft in Sudbury one quarter of the way to the centre of the Earth. Represent the vector using a directed line segment and Cartesian co-ordinates and describe which representation may be more suitable in this situation.

I would show my work but I have no idea where to start.

Answer 1

let the center of the earth be (0,0,0)
find the coordinates of Sudbury. That will give you the tip of the vector pointing out.

The negative of that is the vector pointing in.

Take a look at spherical coordinates and their transformation to rectangular.

You could start here:

https://en.wikipedia.org/wiki/Spherical_coordinate_system