# Vector product

From AMS Glossary

## vector product

(

*Also called*cross product, outer product.) A vector with magnitude equal to the product of the magnitudes of any two given vectors and the sine of the angle between their positive directions.For two vectors then the vector product is the determinant

**A**and**B**, the vector product is often written**A**×**B**(read "**A**cross**B**"), and defines a vector perpendicular to both**A**and**B**and so directed that a right-hand rotation about**A**×**B**through an angle of not more than 180° carries**A**into**B**. The magnitude of**A**×**B**is equal to twice the area of the triangle of which**A**and**B**are coterminous sides. If the vector product is zero, either one of the vectors is zero or the two are parallel. When**A**and**B**are written in terms of their components along the*x*,*y*, and*z*axes of the rectangular Cartesian coordinates, that is,*See*scalar product.