Find the Curvature of the Space Curve A) $\kappa = \frac { 18 } { 13 }$

question 106

Multiple Choice

Find the curvature of the space curve.
- $$\mathbf { r } ( \mathrm { t } ) = 5 \mathrm { ti } + \left( 4 + 8 \cos \frac { 3 } { 2 } \mathrm { t } \right) \mathbf { j } + \left( 4 + 8 \sin \frac { 3 } { 2 } \right) \mathbf { k }$$

• A) \(\kappa = \frac { 18 } { 13 }\)
• B) \(\kappa = \frac { 12 } { 169 }\)
• C) \(\kappa = \frac { 18 } { 169 }\)
• D) \(\kappa = \frac { 12 } { 13 }\)

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Definitions:

Pronation

A rotation of the forearm or hand so that the palm faces downward or backward.

Supination

The rotational movement of the forearm or foot that turns the palm or sole outward or upward.

Dorsiflexion

The action of lifting the foot upwards towards the shin, decreasing the angle between the dorsum of the foot and the leg.

Periodontal Ligament

A group of specialized connective tissue fibers that attach a tooth to the alveolar bone, aiding in tooth stabilization.