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 -
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 -
- [JEE MAIN 2021]
- A
$\cos ^{-1}\left(\frac{n^{2}+1}{n^{2}-1}\right)$
- B
$\cos ^{-1}\left(\frac{{n}^{2}-1}{-{n}^{2}-1}\right)$
- C
$\cos ^{-1}\left(\frac{-n^{2}-1}{n^{2}-1}\right)$
- D
$\cos ^{-1}\left(\frac{n^{2}+1}{n^{2}-1}\right)$
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