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 as a vector using a directed line segment and Cartesian coordinates, we first need to define the direction and magnitude of the vector.

Since the vector represents the path of a drill tip, which is directed towards the center of the Earth, we can represent the direction as pointing downwards. We can choose the positive y-direction to be pointing upwards and the negative y-direction to be pointing downwards. The magnitude of the vector will represent the distance traveled by the drill tip.

Now, let's address the Cartesian coordinates. In a standard Cartesian coordinate system, we have three dimensions: x, y, and z. In this case, we are drilling downwards, so the z-axis can be used to represent the depth.

To represent this vector, we can use a directed line segment pointing downwards along the z-axis. The length of the line segment will represent the distance traveled by the drill tip.

As for which representation may be more suitable in this situation, using Cartesian coordinates and a directed line segment is a good choice because it allows us to express both the direction (downwards) and the magnitude (distance traveled) of the vector. Additionally, using Cartesian coordinates provides a clear and standard way to represent vectors in three-dimensional space.