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The Curvature of the Curve Given by the Vector Function rr

question 27

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The curvature of the curve given by the vector function rr is
k(t) =rt(t) ×rtt(t) rt(t) 3\mathrm { k } ( t ) = \frac { \left| \mathbf { r } ^ { t } ( t ) \times \mathbf { r } ^ { tt } ( t ) \right| } { \left| \mathbf { r } ^ { t } ( t ) \right| ^ { 3 } }
Use the formula to find the curvature of r(t) =(19t,et,et}\mathbf { r } ( t ) = \left( \sqrt { 19 } t , e ^ { t } , e ^ { - t } \right\} at the point (0,1,1) ( 0,1,1 ) .


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