Editing Euclidean vector (section)

===Dot product===
{{main|Dot product}}

The ''dot product'' of two vectors '''a''' and '''b''' (sometimes called the ''[[inner product space|inner product]]'', or, since its result is a scalar, the ''scalar product'') is denoted by '''a'''&nbsp;∙&nbsp;'''b,''' and is defined as:

<math display=block>\mathbf{a}\cdot\mathbf{b}
=\left\|\mathbf{a}\right\|\left\|\mathbf{b}\right\|\cos\theta,</math>

where ''θ'' is the measure of the [[angle]] between '''a''' and '''b''' (see [[trigonometric function]] for an explanation of cosine). Geometrically, this means that '''a''' and '''b''' are drawn with a common start point, and then the length of '''a''' is multiplied with the length of the component of '''b''' that points in the same direction as '''a'''.

The dot product can also be defined as the sum of the products of the components of each vector as

<math display=block>\mathbf{a} \cdot \mathbf{b} = a_1 b_1 + a_2 b_2 + a_3 b_3.</math>