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Regularly Parametrized Curves

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Poirot

Banned
Feb 15, 2012
250
consider y mapping R to R^3 and such that y(0)=(1,0,0) and y'(0)=(0,1,0).

suppose $y''(s)=y(s) * y'(s)$. where * is the cross product

1) show y is a unit speed curve.
2)show that $\frac{d^2}{ds^2}(|y(s)|)=2$
3) deduce $y(s).y'(s)=s$ and further $|y(s)|=(s^2+1)^{0.5}$