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

The curvature of the curve given by the vector function $r$ is $k ( t ) = \frac { \left| \mathbf { r } ^ { \prime } ( t ) \times \mathbf { r } ^ { \prime \prime } ( t ) \right| } { \left| \mathbf { r } ^ { \prime } ( t ) \right| ^ { 3 } }$ Use the formula to find the curvature of $\mathbf { r } ( t ) = \left\langle \sqrt { 13 } t , e ^ { t } , e ^ { - t } \right\rangle$
at the point $( 0,1,1 )$ .

A) $\sqrt { 15 }$
B) $\frac { \sqrt { 2 } } { 15 }$
C) $15 \sqrt { 2 }$
D) $\frac { 15 } { \sqrt { 2 } }$
E) $\frac { \sqrt { 15 } } { 15 }$

Correct Answer:

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