Pre-Quantum Electrodynamics
Cross productc.m.va.cp
\[
{\bf A} × {\bf B} = \left| \begin{array}{ccc} \hat{x} & \hat{y} & \hat{z}
Ax & Ay & Az \\ Bx & By & Bz \end{array} \right|
= \left( Ay Bz - Az By \right) \hat{x} + \left( Bz Ax - Bx Az \right) \hat{y}
- \left( Ax By - Ay Bx \right) \hat{z}
\]
The cross product is distributive:
\[ {\bf A} \times ({\bf B} + {\bf C}) = {\bf A} \times {\bf B} + {\bf A} \times {\bf C} \]
The cross-product is anti-commutative:
\[ {\bf A} \times {\bf B} = - {\bf B} \times {\bf A} \]
this relation making plain that
\[ {\bf A} \times {\bf A} = 0. \]
Created: 2022-02-07 Mon 08:02