Answer
$\frac{3}{5}$
Work Step by Step
See Theorem $12.5 .2 b$
\[
\begin{array}{c}
\kappa(t)=\frac{\left\|\mathrm{r}^{\prime}(t) \times \mathrm{r}^{\prime \prime}(t)\right\|}{\left\|\mathrm{r}^{\prime}(t)\right\|^{3}}=\kappa(0) \\
\mathrm{r}^{\prime}(t)=-2 \sin t \mathrm{i}+3 \cos t \mathrm{j}-\mathrm{k} \quad \mathrm{r}^{\prime}(\pi / 2)=-2 \mathrm{i}-\mathrm{k} \\
\mathrm{r}^{\prime \prime}(t)=-2 \cos t \mathrm{i}-3 \sin t j, \quad \mathrm{r}^{\prime \prime}(\pi / 2)=-3 \mathrm{j} \\
\mathrm{r}^{\prime}(\pi / 2) \times \mathrm{r}^{\prime \prime}(\pi / 2)=\left|\begin{array}{ccc}
i & j & k \\
-2 & 0 & -1 \\
0 & -3 & 0
\end{array}\right|=-3 \mathrm{i}+6 \mathrm{k} \\
\frac{\sqrt{45}}{5^{3 / 2}}=\frac{3 \sqrt{5}}{5^{3 / 2}}=\frac{3}{5}=\kappa(\pi / 2)
\end{array}
\]
