Definition:Vector Cross Product

Definition
Let $\vec u$ and $\vec v$ be $3$-dimensional vectors, such that:
 * $\vec u = u_i \mathbf i + u_j \mathbf j + u_k \mathbf k$
 * $\vec v = v_i \mathbf i + v_j \mathbf j + v_k \mathbf k$

Then the vector cross product, denoted $\vec u \times \vec v$, is defined as:
 * $\vec u \times \vec v = \begin{vmatrix}

\mathbf i & \mathbf j & \mathbf k\\ u_i & u_j & u_k \\ v_i & v_j & v_k \\ \end{vmatrix}$

where $\begin{vmatrix} \ldots \end{vmatrix}$ can be understood as a determinant.

More directly:
 * $\vec u \times \vec v = (u_j v_k - u_k v_j)\mathbf i - (u_i v_k - u_k v_i)\mathbf j + (u_i v_j - u_j v_i)\mathbf k$