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Math Help - Arclength parameterisation

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    Super Member Showcase_22's Avatar
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    Arclength parameterisation

    Let \underline{r} (s):=(f(s),g(s)) be the arclength parameterisation of a plane curve \Gamma \subset \mathbb{R}^2.

    Given \alpha, \beta \in \mathbb{R} such that \alpha^2+\beta^2=1, let \underline{R}(s):=(f(\alpha s), g(\alpha s), \beta s) be a parameterisation of a space curve C \subset \mathbb{R}^3.
    a). Show that \underline{R} is the arclength parameterisation of C.
    I'm not really sure how to show this. Firstly, in my book it has \int_0^t v( \tau)~dt which I can't see how i'm supposed to apply.

    Does anyone have any pointers?
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