Question
Prove that the curve $\mathbf{r}(t)=\langle a \cos t, b \sin t, c \sin t\rangle$ is parameterized by arc lengthprovided $a^{2}=b^{2}+c^{2}=1$
Step 1
This is done by taking the derivative of each component with respect to $t$: \[ \mathbf{r}^{\prime}(t)=\langle-a \sin t, b \cos t, c \cos t\rangle \] Show more…
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