Final answer:
Vectors are usually described in terms of their components in a coordinate system. In two dimensions, a vector describes motion in two perpendicular directions. The reason why the two components must be at 90° to one another is because they represent motion in perpendicular directions.
Step-by-step explanation:
Vectors are usually described in terms of their components in a coordinate system. In two dimensions, a vector describes motion in two perpendicular directions, such as vertical and horizontal. Every 2D vector can be expressed as a sum of its x and y components. Components along the same axis can be added to one another, making it easier to work with vectors. However, the reason why the two components must be at 90° to one another is because they represent motion in perpendicular directions. If the components were at 60° apart, they would not represent motion in perpendicular directions.
For example, if we have a vector with components in the x-axis and y-axis, if the components were at 60° apart, it would represent a combination of motion in the x-axis and a different direction that is not perpendicular to it, resulting in an inaccurate representation of the motion. A sketch can be drawn to illustrate this by drawing a vector with components at 90° and at 60° apart, and demonstrating how the 90° components represent motion in a perpendicular manner, while the 60° components do not.