Math & Kinematics

Cross Product

The cross product is a binary operation on two vectors in R3 producing a vector perpendicular to both, with magnitude equal to the parallelogram area they span and direction given by the right-hand rule. In robotics it computes torque as r cross F, angular momentum, and velocity of rotating points, and its skew-symmetric matrix form underlies the Jacobian columns of revolute joints and the algebra of rotations in se(3).

Why it matters for physical AI

Torque computation, Jacobian construction, and rigid-body dynamics all reduce to cross products, so the operation appears in virtually every kinematics and dynamics routine executing on a robot.