Exercise 18

  1. Find the unit tangent and unit normal vectors \(\mathbf{T}(t)\) and \(\mathbf{N}(t)\).
  2. Use Formula 9 to find the curvature. \(\mathbf{r}(t) = \langle t^2, \sin t - t\cos t, \cos t + t\sin t \rangle, t > 0\)