Magnitude
The length of the vector calculated using the Pythagorean theorem.
|v| = √(x² + y²)
Vector Formulas
Direction
The angle the vector makes with the positive x-axis.
θ = atan2(y, x)
Addition
Add corresponding x and y components.
(x₁ + x₂, y₁ + y₂)
Dot Product
The product of vector magnitudes and the cosine of the angle between them.
x₁x₂ + y₁y₂