Ket vectors in three-dimensional space and their cross product

In quantum mechanics, the ket notation for vectors was introduced in 1939 by Paul Dirac for describing the quantum states. In this framework, the dot product was easily rendered as a bra-ket operation. Here, we show that it is also possible to represent the cross product of vectors within this notation. We will consider the case of Euclidean vectors in a three-dimensional space with orthonormal basis vectors