Find the Curvature of the Space Curve A) $\kappa = \frac { 1 } { 30 } \sqrt { \frac { 2 } { 1 + t ^ { 2 } } }$

question 87

Multiple Choice

Find the curvature of the space curve.
- $$\mathbf { r } ( \mathrm { t } ) = \frac { 40 } { 9 } ( 1 + t ) ^ { 3 / 2 } \mathbf { i } + \frac { 40 } { 9 } ( 1 - t ) ^ { 3 / 2 } \mathbf { j } + \frac { 10 } { 3 } t \mathbf { k }$$

• A) \(\kappa = \frac { 1 } { 30 } \sqrt { \frac { 2 } { 1 + t ^ { 2 } } }\)
• B) \(\kappa = \frac { 1 } { 30 } \sqrt { \frac { 2 } { 1 - t ^ { 2 } } }\)
• C) \(\kappa = \frac { 1 } { 3 } \sqrt { \frac { 2 } { 1 - t ^ { 2 } } }\)
• D) \(\kappa = \frac { 1 } { 3 } \sqrt { \frac { 2 } { 1 + t ^ { 2 } } }\)

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