Rotation of Coordinate Axes

In this lesson,  we shall begin with vectors as geometrical objects.
A quick review of a few  vector algebra identities will be presented.
With a choice of coordinate system, vectors are described as objects with
three components. We will present a result  on change in components
of a vector when coordinate axes are changed.

A first exposure to vector algebra; Dot, cross and triple  products.
Components of a vector along coordinate axes.

\begin{enumerate}
\item For a quick review of vector algebra see Murphy\cite{Murphy} Ch4;
Griffiths\cite{Griff:EM} Ch1; For use of vectors in Physics see Feynman
Lectures Vol-I\cite{Feyn1} Ch 11.

\item
The matrix \(R\) relating  components of a vector in two different coordinate
systems is an orthogonal matrix, see Eqs.\eqref{me-lec-02006;EQ12} -
\eqref{me-lec-02006;EQ14}.
\end{enumerate}
\paragraph*{Properties of orthogonal matrices}
\input{mat-srf-01001}
\paragraph*{References}
\href{https://www.youtube.com/watch?v=QudbrUcVPxk}{\HighLight[LightCyan]{Watch
this video}} to get started on definition of groups.

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