Pre-Quantum Electrodynamics

Vectors will always be denoted by bold symbols, e.g. \({\bf A}\). Component notation (in \({\mathbb R}^3\) with cartesian coordinates):

\[ {\bf A} = \left( \begin{array}{c} A_x \\ A_y \\ A_z \end{array}\right) \]

Commutativity and associativity of vector addition

\[ {\bf A} + {\bf B} = {\bf B} + {\bf A}, \hspace{10mm} ({\bf A} + {\bf B}) + {\bf C} = {\bf A} + ({\bf B} + {\bf C}) \]

Distributivity of multiplication by a scalar

\[ c ({\bf A} + {\bf B}) = c{\bf A} + c{\bf B} \]