How to Use the 2D Vector Calculator
Enter the components of vectors A(ax, ay) and B(bx, by) to instantly get magnitude, addition, subtraction, dot product, cross product, and the angle between them.
Key Formulas
Magnitude: |A| = √(ax² + ay²)
Dot product: A·B = ax·bx + ay·by
Cross product (2D scalar): A×B = ax·by − ay·bx
Angle: θ = arccos(A·B / (|A|·|B|))
FAQ
What if I enter a zero vector?
A zero vector has no direction, so the angle between it and another vector is undefined. The calculator will display "Undefined (zero vector)".
How do I get the unit vector?
Unit vector = A / |A| = (ax/|A|, ay/|A|). Divide each component by the magnitude shown in the results.