Definition:Vector Cross Product/Definition 2

Definition
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:
 * $\mathbf a \times \mathbf b = \left\Vert{\mathbf a}\right\Vert \, \left\Vert{\mathbf b}\right\Vert \sin \theta \hat {\mathbf n}$

where:
 * $\left\Vert{\mathbf a}\right\Vert$ 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.


 * VectorCrossProduct.png

Also see

 * Equivalence of Definitions of Vector Cross Product