2D & 3D Vector Calculator

Vectors represent directional physical quantities including velocity, acceleration, force, magnetic fields, and 3D surface normals in video game graphics and robotics kinematics.

This tool computes the Euclidean magnitude of vectors in 2D or 3D space, their dot product (scalar projection), cross product (orthogonal normal vector in 3D), and the exact angle between them in degrees.

Magnitude |u| = √(x² + y² + z²). Dot product u · v = u₁v₁ + u₂v₂ + u₃v₃. Angle θ = arccos((u · v) / (|u||v|)). Cross product u × v generates the determinant-based orthogonal vector.