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Active Calculus - Multivariable

Activity 10.6.3.
Compute the splitting of the acceleration for the curve given by \(\vr(t)= \langle t, \frac{t^2}{2},\frac{t^3}{6} \rangle\) at \(t=1\text{.}\) You should calculate \(a_{\vT}\text{,}\) \(a_{\vN}\text{,}\) \(\vT\text{,}\) and \(\vN\text{.}\) Additionally, you should verify \(\va = a_{\vT} \vT +a_{\vN} \vN \) and that \(\vT\) is orthogonal to \(\vN\text{.}\)