### 2.2.7 Vector product, scalar triple product

The angle θ between two vectors u and v in ${\epsilon}^{3}$ is defined by

$\text{cos}\theta =\frac{\mathbf{u}\xb7\mathbf{v}}{\left|\mathbf{u}\right|\left|\mathbf{v}\right|},$

(2.54)

where |u| is the natural norm, i.e., |u| = (u · u)^{1/2}. Then the vector product in ${\epsilon}^{3}$ is defined by

$\mathbf{u}\times \mathbf{v}=\left|\mathbf{u}\right|\left|\mathbf{v}\right|\mathbf{n}\text{sin}\theta ,\left|\mathbf{n}\right|=1,\mathbf{u}\xb7\mathbf{n}=\mathbf{v}\xb7\mathbf{n}=0.$

(2.55)

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

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