What is the cross product of two perpendicular vectors and how is it calculated?

The cross product of two perpendicular vectors is a vector that is perpendicular to both of the original vectors. It is calculated using the formula:

mathbfa times mathbfb beginpmatrix a2b3 - a3b2 a3b1 - a1b3 a1b2 - a2b1 endpmatrix

Where (mathbfa beginpmatrix a1 a2 a3 endpmatrix) and (mathbfb beginpmatrix b1 b2 b3 endpmatrix) are the two perpendicular vectors.