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{{math-h}}

{{math-h}}

In the <math>n</math>-dimensional [[Euclidean vector space]] <math>\mathbb{R}^n</math>, the '''dot product''' is defined for two [[Vector|vectors]] <math>\vec{x} =

In the <math>n</math>-dimensional [[Euclidean vector space]] <math>\mathbb{R}^n</math>, the '''dot product''' is defined for two [[vector]]s <math>\vec{x} =

\langle x_1, \ldots, x_n \rangle</math> and <math>\vec{y} = \langle y_1, \ldots, y_n \rangle</math> as follows:

\langle x_1, \ldots, x_n \rangle</math> and <math>\vec{y} = \langle y_1, \ldots, y_n \rangle</math> as follows:

== Application ==

== Application ==

The [[dot product]] is useful in projecting one vector onto another, as in calculating the work done by applying a force to a particle.  If you know the dot product of two vectors, then you can easily calculate the angle between the vectors.

The dot product is useful in projecting one vector onto another, as in calculating the work done by applying a force to a particle.  If you know the dot product of two vectors, then you can easily calculate the angle between the vectors.

The dot product can also be used to find other values through application of the [[Stokes' Theorem]] and other theorems.

The dot product can also be used to find other values through application of the [[Stokes' Theorem]] and other theorems.

[[Category:Linear algebra]]

[[Category:Linear algebra]]

[[Category:vector analysis]]

[[Category:Vector analysis]]

[[Category:calculus]]

[[Category:Calculus]]

[[Category:mathematics]]

[[Category:Mathematics]]

[[category:physics]]

[[Category:Physics]]