$\newcommand{\DD}[2][]{\frac{d^2 #1}{d^2 #2}}$
$\newcommand{\matrixelement}[3]{\langle#1|#2|#3\rangle}$
$\newcommand{\PP}[2][]{\frac{\partial^2 #1}{\partial #2^2}}$
$\newcommand{\dd}[2][]{\frac{d#1}{d#2}}$
$\newcommand{\pp}[2][]{\frac{\partial #1}{\partial #2}}$
$\newcommand{\average}[2]{\langle#1|#2|#1\rangle}$
$\newcommand{\xbf}{\bf x}$
Let \(\xbf\) denote the position vector \(\overrightarrow{OP}\) of a point \(P\). Under a rotation of the vector about by an angle \(\theta\) about an axis \(\hat{n}\), the vector \(\xbf\) becomes a vector \(\xbf{'}\) pointing to a new position \(Q\). There are three methods which can be used to relate components of a vector \(\xbf\) and the rotated vector \(\xbf{'}\).
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4727:Diamond Point