Solved: Using (22), show that if C is represented by ret)

Chapter 9, Problem 9.1.187

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Using (22), show that if C is represented by rít) with arbitrary t, then

\(\kappa(t)=\frac{\sqrt{\left(\mathbf{r}^{\prime} \cdot \mathbf{r}^{\prime}\right)\left(\mathbf{r}^{\prime \prime} \cdot \mathbf{r}^{\prime \prime}\right)-\left(\mathbf{r}^{\prime} \cdot \mathbf{r}^{\prime \prime}\right)^{2}}}{\left(\mathbf{r}^{\prime} \cdot \mathbf{r}^{\prime}\right)^{3 / 2}}\)

Text Transcription:

k(t)=sqrt (r’ times r’)(r’’ times r’’)-(r’ times r’’)^2/(r’ times r’)3/2

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