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!
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.
The second format, where the vector is represented by (3/4) R, is more suitable in this situation because it provides a more concise and meaningful representation of the path of the drill tip.
Cartesian coordinates represent the location of a point in space using three numerical values along the x, y, and z axes. While this representation can be useful for indicating the initial and final positions of the drill tip, it does not specifically convey the information about the direction and magnitude of the vector.
On the other hand, representing the vector as (3/4) R provides a clear indication of both the direction and the magnitude of the vector. The magnitude, in this case, is three-fourths of the radius of the Earth, denoted by R. This representation is more suitable because it explicitly communicates the length and direction of the drill path.