In mathematics, vector multiplication may refer to one of several operations between two (or more) vectors. It may concern any of the following articles:

• Dot product – also known as the "scalar product", a binary operation that takes two vectors and returns a scalar

• Cross product – also known as the "vector product", a binary operation on two vectors that results in another vector

• Exterior product or wedge product – a binary operation on two vectors that results in a bivector) but generalizes to arbitrary affine spaces and products between more than two vectors.

• Tensor product are vector spaces, their tensor product belongs to the tensor product of the vector spaces.

• Geometric product or Clifford product is a mixed quantity consisting of a scalar plus a bivector. The geometric product is well defined for any multivectors as arguments.

• A bilinear product in an algebra over a field.

• A Lie bracket for vectors in a Lie algebra.

• Hadamard product – entrywise or elementwise product of tuples.

• Outer product matrix.

• Triple products – products involving three vectors.

• Quadruple products – products involving four vectors.

Applications

Vector multiplication has multiple applications in regards to mathematics, but also in other studies such as physics and engineering.

Physics

• The cross product occurs frequently in the study of rotation, where it is used to calculate torque and angular momentum. It can also be used to calculate the Lorentz force exerted on a charged particle moving in a magnetic field.

• The dot product is used to determine the work done by a constant force.

See also

• Scalar multiplication

• Matrix multiplication

• Vector addition

• Vector algebra relations