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boombaby
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Homework Statement
suppose f is a differentiable mapping of R1 into R3 such that |f(t)|=1 for every t. Prove that [tex]f'(t)\cdot f(t)=0[/tex].
I guess it is more proper to write [tex](\nabla f)(t) \cdot f(t)=0[/tex], where [tex](\nabla f)(t)[/tex] is the gradient of f ant t.
Homework Equations
The Attempt at a Solution
it is then equivalent to prove [tex]\sum\;(Df_{i})(t)\cdot f_{i}(t)=0[/tex], but I've no idea of how to use the |f(t)|=1 to deduce the disired results, although the equation has an easy geometrically interpretation
Any hint may help, thanks a lot.
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