Angle between two curves first fundamental form and chain rule

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enter image description here Here $r_1$ is in terms of $u_1$ and $r_2$ in terms of $u_2$, how can they write $E$ when we have dot product of $r_1$ with respect to $u_1$ and $r_2$ with respect to $u_2$. We can write $E$ only when they are the same right?