JEE Physics Practice Question

Two vectors $$\overrightarrow X $$ and $$\overrightarrow Y $$ have equal magnitude. The magnitude of ($$\overrightarrow X $$ $$-$$ $$\overrightarrow Y $$) is n times the magnitude of ($$\overrightarrow X $$ + $$\overrightarrow Y $$). The angle between $$\overrightarrow X $$ and $$\overrightarrow Y $$ is :

1. A.$${\cos ^{ - 1}}\left( {{{ - {n^2} - 1} \over {{n^2} - 1}}} \right)$$
2. B.$${\cos ^{ - 1}}\left( {{{{n^2} - 1} \over { - {n^2} - 1}}} \right)$$
3. C.$${\cos ^{ - 1}}\left( {{{{n^2} + 1} \over { - {n^2} - 1}}} \right)$$
4. D.$${\cos ^{ - 1}}\left( {{{{n^2} + 1} \over {{n^2} - 1}}} \right)$$