Overview
{% \vec{A} \times \vec{B} = AB \; sin \theta \; \hat{n} %}
where {% \hat{n} %} is the unit normal vector pointing perpendicular to the plane containing both {% \vec{A} %}
and {% \vec{B} %}.
{% \vec{A} \times (\vec{B} + \vec{C}) = (\vec{A} \times \vec{B}) + (\vec{A} \times \vec{C}) %}
{% (\vec{A} \times \vec{B}) = -(\vec{B} \times \vec{A}) %}
Component Form
{% \vec{A} \times \vec{B} = (A_yB_z - A_z B_y)\hat{x} + (A_zB_x - A_xB_z)\hat{t} + (A_xB_y - A_yB_x) \hat{z} %}
which can be represented as a
matrix determinant
{%
\begin{vmatrix}
\hat{x} & \hat{y} & \hat{z} \\
A_x & A_y & A_z \\
B_x & B_y & B_z \\
\end{vmatrix}
%}