Summer School Calculus
posted by Derek .
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!
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.