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.
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
To represent the path of the drill tip using a vector, we need to consider the direction and magnitude of the displacement. Since the drill tip is moving towards the center of the Earth, the direction of the vector will be pointing downwards.
Since we are given that the drill tip goes one-quarter of the way to the center of the Earth, we can say that the magnitude of the displacement is 1/4 of the distance from the starting point to the center of the Earth. Let's assume this distance is "d".
Using Cartesian coordinates, we can represent the vector as (0, -1/4d). The first component of the vector (0) indicates that there is no displacement in the horizontal direction, and the second component (-1/4d) indicates the displacement in the vertical (downward) direction.
Now, let's consider which representation - the directed line segment or Cartesian coordinates - may be more suitable in this situation.
The directed line segment is a visual representation where the vector is drawn as an arrow starting from the initial point and ending at the terminal point. It provides a clear visualization of the direction and magnitude of the vector.
In this case, the directed line segment representation might not be the most suitable because it would be challenging to accurately draw a line segment representing a drill shaft that goes one-quarter of the way to the center of the Earth. The scale and accuracy of such a diagram would be difficult to achieve.
On the other hand, the Cartesian coordinate representation provides a concise and precise numerical representation of the vector. It is easy to understand and calculate with the coordinates, and it eliminates the need for complex diagrams.
Therefore, in this situation, the Cartesian coordinate representation may be more suitable for representing the vector which describes the path of the drill tip.