How this calculator works
Enter vector a x, vector a y, vector b x, vector b y. CalcStack applies the displayed formula and reports each intermediate planning value with the units shown.
Formula / method
Magnitude = √(x²+y²); dot product = x₁x₂+y₁y₂; cos θ = dot/(|A||B|)
Worked example
Use the documented default inputs to model vector magnitude & direction.
Assumptions and limitations
Inputs represent stable average operating conditions and the displayed equation applies.
This is a planning model; real systems and measurements can require domain-specific corrections.