The vector cross product (or simply vector product, as
opposed to the scalar product (which is also called the
dot product, or inner product)) is commonly used in
vector calculus--a basic mathematical toolset used in
acoustics , electromagnetism , quantum
mechanics, and more. It can be defined symbolically in the form of
a matrix determinant:B.19
The second and third lines of Eq. (B.15) make it clear that . This is one example of a host of identities that one learns in vector calculus and its applications.