For the helix r(t)=⟨3cos(t),3sin(t),4t⟩\mathbf{r}(t) = \langle 3\cos(t), 3\sin(t), 4t \rangler(t)=⟨3cos(t),3sin(t),4t⟩, find the curvature κ\kappaκ using the formula κ=∣r′×r′′∣∣r′∣3\kappa = \frac{|\mathbf{r}' \times \mathbf{r}''|}{|\mathbf{r}'|^3}κ=∣r′∣3∣r′×r′′∣.
κ=325\kappa = \frac{3}{25}κ=253
κ=15\kappa = \frac{1}{5}κ=51
κ=35\kappa = \frac{3}{5}κ=53
κ=3\kappa = 3κ=3