When should we resolve vectors?

Vectors can be resolved generally into any two non-parallel directions. These are done more as rectangular components using unit vectors. The latter is most common in physics and engineering to represent them into Cartesian coordinates for simplified vector operations.

Vector resolution is important to break complex motion into simpler, one-dimensional components. With it, we can simplify vector addition and analysis in 2D or 3D motion. Generally, we rely on perpendicular directions. That makes vector operations with displacement, velocity, and acceleration more manageable and accurate.