Find the Curvature of the Space Curve $$r ( t ) = - 5 i + ( 4 + 2 t ) j + \left( t ^ { 2 } + 8 \right) \mathbf { k }$$

Multiple Choice

Find the curvature of the space curve.
- $$r ( t ) = - 5 i + ( 4 + 2 t ) j + \left( t ^ { 2 } + 8 \right) \mathbf { k }$$

A) $\kappa = \frac { 1 } { 2 \left( t ^ { 2 } + 1 \right) ^ { 3 / 2 } }$
B) $\kappa = - \frac { 1 } { 2 \left( t ^ { 2 } + 1 \right) ^ { 3 / 2 } }$
C) $\kappa = \frac { 1 } { 2 \sqrt { t ^ { 2 } + 1 } }$
D) $\kappa = \frac { 1 } { \left( t ^ { 2 } + 1 \right) ^ { 3 / 2 } }$