Resolution of Vectors

Vector resolution is important when analysing motion in two or three dimensions. It's used in vector addition and subtraction, projectile motion, and expressing velocity or acceleration using component form. Resolution with unit vectors also helps in applying kinematic equations to multidimensional problems. 

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.