a
\(\begin{array}{*{20}{l}} {\left| {\vec A + \vec B} \right| = n\left| {\vec A - \vec B} \right|} \\ { \Rightarrow \,{A^2} + {B^2} + 2AB\,\cos \,\theta } \\ {\,\,\,\,\,\,\, = {n^2}\left( {{A^2} + {B^2} - 2AB\,\cos \,\theta } \right)} \\ { \Rightarrow \,\cos \,\theta \,\left( {1 + {n^2}} \right) = \frac{{2{a^2}\left( {{n^2} - 1} \right)}}{{2{a^2}}}\,\,} \\ {[A = B = c]} \\ {\cos \,\theta = \frac{{{n^2} - 1}}{{{n^2} + 1}}} \end{array}\)