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Given two normalized vectors \(\chi_1\) and \(\chi_2\):
\begin{equation}
\chi_1=\begin{pmatrix}\cos\alpha\\ \sin\alpha\end{pmatrix}\qquad
\chi_2=\begin{pmatrix}\cos\beta\\ \sin\beta\end{pmatrix},
\end{equation}
find conditions on \(\alpha,\beta \) so that \(\chi_1+\chi_2\) may be a normalized vector.
Answer : \(\alpha-\beta=\frac{2\pi}{3}, or \frac{4\pi}{3}\)
Source: W.H. Steeb*
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