r×q

r×q is a mathematical operation that represents the cross product of two vectors, r and q. The cross product is a binary operation that takes two vectors in three-dimensional space and returns a vector that is perpendicular to both of the original vectors. The direction of the resulting vector is determined by the right-hand rule, and its magnitude is equal to the area of the parallelogram spanned by the two input vectors.

The cross product is not commutative, meaning that r×q is not necessarily equal to q×r. In fact, r×q = -(q×r). It is, however, distributive over vector addition, so r×(q+s) = r×q + r×s. The cross product is only defined for vectors in three-dimensional space.

The cross product has applications in various fields of physics and engineering, including mechanics, electromagnetism, and fluid dynamics. For instance, in mechanics, the torque of a force F applied at a position vector r from a pivot point is given by τ = r×F. In electromagnetism, the force on a charged particle moving with velocity v in a magnetic field B is given by F = q(v×B), where q is the charge of the particle.