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.
To represent the path of a drill tip using a vector, we need to specify both the magnitude and direction of the vector. In this case, the vector represents the path of the drill tip, which is a directed line segment from the starting point to the end point.
Using Cartesian coordinates, we can represent the vector by specifying the x, y, and z components. Let's denote the starting point as (0, 0, 0) and the end point as (x, y, z). The vector can be written as:
𝑉 = (x, y, z)
Now, in this situation where the drill tip is being used to bore a deep mine shaft, the vector representation using Cartesian coordinates may be more suitable. This is because Cartesian coordinates provide a clear and systematic way of representing the direction and magnitude of the path.
Alternatively, we could also represent the vector using direction cosines or spherical coordinates, but these representations may not be as intuitive or convenient in this particular scenario. Cartesian coordinates provide a straightforward way of visualizing and understanding the path of the drill tip.