The curvature of the curve given by the vector function $r$ is
$$k ( t ) = \frac { \left| \mathbf { r } ^ { t } ( t ) \times \mathbf { r } ^ { tt } ( t ) \right| } { \left| \mathbf { r } ^ {t } ( t ) \right| ^ { 3 } }$$ Use the formula to find the curvature of $\mathbf { r } ( t ) = \left( \sqrt { 19 } t , e ^ { t } , e ^ { - t } \right\}$ at the point $( 0,1,1 )$.
A) $\sqrt { 21 }$
B) $\frac { \sqrt { 2 } } { 21 }$
C) $21 \sqrt { 2 }$
D) $\frac { 21 } { \sqrt { 2 } }$
E) $\frac { \sqrt { 21 } } { 21 }$

Question

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The Answer of The curvature of the curve given by the vector function $r$ is
$$k ( t ) = \frac { \left| \mathbf { r } ^ { t } ( t ) \times \mathbf { r } ^ { tt } ( t ) \right| } { \left| \mathbf { r } ^ {t } ( t ) \right| ^ { 3 } }$$ Use the formula to find the curvature of $\mathbf { r } ( t ) = \left( \sqrt { 19 } t , e ^ { t } , e ^ { - t } \right\}$ at the point $( 0,1,1 )$.
A) $\sqrt { 21 }$
B) $\frac { \sqrt { 2 } } { 21 }$
C) $21 \sqrt { 2 }$
D) $\frac { 21 } { \sqrt { 2 } }$
E) $\frac { \sqrt { 21 } } { 21 }$

The Curvature of the Curve Given by the Vector Function rrr

The Curvature of the Curve Given by the Vector Function $r$