Editing Product (mathematics) (section)

===Cross product in 3-dimensional space===
{{main|Cross product}}
The [[cross product]] of two vectors in 3-dimensions is a vector perpendicular to the two factors, with length equal to the area of the parallelogram spanned by the two factors.

The cross product can also be expressed as the [[formal calculation|formal]]{{Efn|Here, "formal" means that this notation has the form of a determinant, but does not strictly adhere to the definition; it is a mnemonic used to remember the expansion of the cross product.}} [[determinant]]:
:<math>\mathbf{u \times v} = \begin{vmatrix}
  \mathbf{i} & \mathbf{j} & \mathbf{k} \\
         u_1 &        u_2 &        u_3 \\
         v_1 &        v_2 &        v_3 \\
\end{vmatrix}</math>