# cross

Vector

#### synopsis

Compute the cross product between two vectors, defined as the vector perpendicular to both input vectors, with its direction defined by the right-hand rule.

$$\mathbf{a}\times\mathbf{b}=\left(a_{y}b_{z}-a_{z}b_{y}\,,\quad a_{z}b_{x}-a_{x}b_{z}\,,\quad a_{x}b_{y}-a_{y}b_{x}\right)$$

The length of the cross product can be interpreted geometrically as:

$$\left\Vert \mathbf{a}\times\mathbf{b} \right\Vert=\left\Vert \mathbf{a}\right\Vert \left\Vert \mathbf{b}\right\Vert \sin\theta$$

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