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**Homework Statement::**.

**Relevant Equations::**.

Generally, when we talk about preservation of angle between two vectors, we talk about conformal transformation. But what is confusing me is, shouldn't any general transformation of coordinates preserve the angle between two vectors?

What i mean is: The expression for the angle is given by $$cos(\theta) = \frac{ V^{\mu}U^{v} g_{\mu v}}{\sqrt{(V^{a}V^{b} g_{ab})(U^{r}U^{s} g_{rs})}}$$

Isn't it automatically invariant? So why do we bother to study in detail (even given them a name, conformal transformation), if all transformation preserves it after all?