Motion in a Plane — Formula Sheet

Displacement vector = final position vector - initial position vector

Unit vector: Â = A / A

Rectangular component form: A = Ax i + Ay j

Magnitude in 3D: |A| = sqrt(Ax^2 + Ay^2 + Az^2)

R = sqrt(A^2 + B^2 + 2AB cosθ)

tan α = (B sinθ) / (A + B cosθ)

Ax = A cosθ

Ay = A sinθ

A = sqrt(Ax^2 + Ay^2)

θ = tan^-1(Ay / Ax)

The unit vector along A is written as A_hat = A / A.