### 2.2.7 Vector product, scalar triple product

The angle θ between two vectors u and v in $ε3$ is defined by

$\text{cos}\theta =\frac{\mathbf{u}·\mathbf{v}}{|\mathbf{u}||\mathbf{v}|},$

(2.54)

where |u| is the natural norm, i.e., |u| = (u · u)1/2. Then the vector product in $ε3$ is defined by

$\mathbf{u}×\mathbf{v}=|\mathbf{u}||\mathbf{v}|\mathbf{n}\text{sin}\theta ,|\mathbf{n}|=1,\mathbf{u}·\mathbf{n}=\mathbf{v}·\mathbf{n}=0.$

(2.55)

As such, the vector product accepts two vectors u and v as inputs, and provides ...

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