Question

I don't know how to answer this: 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. Thanks a bunch!

drwls posted this: If x,y,z are coordinates of the mine opening at a point on the surface of the Earth (radius R), then they satisfy x^2 + y^2 + z^2 = R^2.

In this case, the coordinates of the other end of the mine line segment are 0.75 x, 0.75 y, 0.75 z. That may satisy your "Cartesian representation" question.

If the vector from the center of the Earth to the mine opening is R (which should be in boldface type or with an arrow above to denote a vector), then (3/4) R is a vector denoting the tunnel line segment.

The second format appears more suitable.


My issue: Why is the second format more suitable? Thanks again!

Answer 1

Because it is easier to write down. Your summer course in calculus is being taught in a way that seems to be more about "conceptual math" than teaching the basics. I learned calculus over 50 years ago, am not used to this kind of teaching, and will not be responding to posts that are about opinions and which involve "new math" jargon and notations that I am not familiar with.