Editing Vector calculus (section)

== Vector algebra ==
{{main|Euclidean vector#Basic properties}}
The algebraic (non-differential) operations in vector calculus are referred to as ''vector algebra'', being defined for a vector space and then applied [[pointwise]] to a vector field. The basic algebraic operations consist of:

{| class="wikitable" style="text-align:center"
|+Notations in vector calculus
|-
!scope="col"|Operation
!scope="col"|Notation
!scope="col"|Description
|-
![[Vector addition]]
|<math>\mathbf{v}_1 + \mathbf{v}_2</math>
|Addition of two vectors, yielding a vector.
|-
!scope="row"|[[Scalar multiplication]]
|<math>a \mathbf{v}</math>
|Multiplication of a scalar and a vector, yielding a vector.
|-
!scope="row"|[[Dot product]]
|<math>\mathbf{v}_1 \cdot \mathbf{v}_2</math>
|Multiplication of two vectors, yielding a scalar.
|-
!scope="row"|[[Cross product]]
|<math>\mathbf{v}_1 \times \mathbf{v}_2</math>
|Multiplication of two vectors in <math>\mathbb R^3</math>, yielding a (pseudo)vector.
|}

Also commonly used are the two [[triple product]]s:
{| class="wikitable" style="text-align:center"
|+Vector calculus triple products
|-
!scope="col"|Operation
!scope="col"|Notation
!scope="col"|Description
|-
!scope="row"|[[Scalar triple product]]
|<math>\mathbf{v}_1\cdot\left( \mathbf{v}_2\times\mathbf{v}_3 \right)</math>
|The dot product of the cross product of two vectors.
|-
!scope="row"|[[Vector triple product]]
|<math>\mathbf{v}_1\times\left( \mathbf{v}_2\times\mathbf{v}_3 \right)</math>
|The cross product of the cross product of two vectors.
|}