Chapter 12.5, Problem 10ES

To determine

To calculate: The curvature of $\kappa \left(t\right)$ at the vector, $r\left(t\right)=ti+\frac{1}{2}{t}^{2}j+\frac{1}{3}{t}^{3}k$ , by using the formula, $\kappa \left(t\right)=\frac{‖r^{\prime }\left(t\right)\times r^{″}\left(t\right)‖}{{‖r^{\prime }\left(t\right)‖}^3}$ .