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

question 31

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) \(\kappa = \frac { 1 } { \left( t ^ { 2 } + 1 \right) ^ { 3 / 2 } }\)

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