Definition:Vector Cross Product/Definition 2

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Let $\mathbf a$ and $\mathbf b$ be vectors in a vector space $\mathbf V$ of $3$ dimensions.

The vector cross product, denoted $\mathbf a \times \mathbf b$, is defined as:

$\mathbf a \times \mathbf b = \norm {\mathbf a} \norm {\mathbf b} \sin \theta \, \mathbf {\hat n}$


$\norm {\mathbf a}$ denotes the length of $\mathbf a$
$\theta$ denotes the angle from $\mathbf a$ to $\mathbf b$, measured in the positive direction
$\hat {\mathbf n}$ is the unit vector perpendicular to both $\mathbf a$ and $\mathbf b$ in the direction according to the right-hand rule.

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