# Dot Product

- The dot product of two vectors is obtained by adding the products of the respective components of the vectors.

- The dot product of two vectors:

- is represented and calculated as:

**Commutative law**

**Distributive law**

- also

- The dot product of a vector with itself is the square of the magnitude:

- Note:
- if
**A**=0 and only if**A**=0

**Cauchy-Schwarz Inequality**- The dot product of two vectors cannot be greater in magnitude than the product of the magnitudes of the vectors.

**See also: **Vector.

**Subjects: ** Algebra