# Almost orthogonality of independent random vectors [closed]

If $$X_1$$ and $$X_2$$ are two independent isotropic random vectors in $$\mathbb{R}^n$$, then $$\mathbb{E}\|X_i\|_{2}^{2}=n$$, $$\mathbb{E}\langle X_1,X_2\rangle^{2}=n$$.

How can I show from the above result that in high dimensional spaces, independent and isotropic random vectors are almost orthogonal?

## closed as off-topic by Carlo Beenakker, Jan-Christoph Schlage-Puchta, Boris Bukh, Mark Wildon, Neil HoffmanJan 3 at 18:02

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