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Section 12.10 : Curvature

Find the curvature for each the following vector functions.

1. \(\vec r\left( t \right) = \left\langle {5t,1 - 2t,4{t^{\frac{3}{2}}}} \right\rangle \)
2. \(\vec r\left( t \right) = \left\langle {6,{{\bf{e}}^{ - 5t}},3t{{\bf{e}}^{ - 5t}}} \right\rangle \)
3. \(\vec r\left( t \right) = \left\langle {\cos \left( {\omega t} \right),t,\sin \left( {\omega t} \right)} \right\rangle \)