Find the Curvature $K$ Of the Curve $\mathbf { r } ( t ) = \langle \sin 2 t , 3 t , \cos 2 t \rangle \text { when } t = \frac { \pi } { 2 }$

Multiple Choice

Find the curvature $K$ of the curve $\mathbf { r } ( t ) = \langle \sin 2 t , 3 t , \cos 2 t \rangle \text { when } t = \frac { \pi } { 2 }$

A) $\frac { 3 } { 13 }$

B) $\frac { 4 } { 13 }$
C) $\frac { 6 } { 13 }$
D) $\frac { 8 } { 13 }$
E) $\frac { 1 } { 3 }$
F) $\frac { 4 } { 9 }$

G) $\frac { 2 } { 3 }$

H) $\frac { 8 } { 9 }$