Kirk Morgan
12/18/2023 · High School
(a) Determine los vectores tangente unitario y normal unitari \( \mathrm{T}(t) \) y \( \mathrm{N}(t) \). (b) Usc la fórmula 9 para determinar la curvatura. 19. \( \mathrm{r}(t)=\left\langle\sqrt{2} t, e^{t}, e^{-1}\right\rangle \)
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Para encontrar los vectores tangente y normal unitarios y la curvatura de \(\mathbf{r}(t) = \langle \sqrt{2} t, e^{t}, e^{-1} \rangle\), primero calcula la derivada del vector de posición, luego normaliza esta derivada para obtener el vector tangente unitario. Posteriormente, calcula la segunda derivada y normaliza la derivada del vector tangente para obtener el vector normal unitario. Finalmente, usa la fórmula de curvatura \(\kappa = \frac{\|\mathbf{T}'(t)\|}{\|\mathbf{r}'(t)\|^3}\) para encontrar la curvatura.
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