Electricity and magnetism/Magnetism/The vector product

To calculate the magnetic forces produced by moving charges and the magnetic forces exerted on moving charges, one must know the cross product of two vectors in three-dimensional space: The vector product w = u×v of two vectors u and v is the vector whose length is uv sin where is the angle between u and v, u and v are the lengths of u and v, whose direction is perpendicular to u and v such that the triplet u, v, w is positively oriented. File:Cross-product-simple.svg The triplet (thumb, index, middle finger) of the right hand is positively oriented. The one of the left hand is negatively oriented. (right, front, above) is positively oriented. In general, the x, y and z axes of a coordinate system are chosen positively oriented. 300px The cross product of two vectors with the same direction is the zero vector. The length of the cross product of two perpendicular vectors is the product of their lengths.