The Torsion of a Curve Defined By $\mathbf { r } ( t )$

question 69

Multiple Choice

The torsion of a curve defined by $\mathbf { r } ( t )$ is given by
$$\tau = \frac { \left( \mathbf { r } ^ { t } \times \mathbf { r } ^ {tt } \right) \cdot \mathbf { r } ^ { ttt } } { \left| \mathbf { r } ^ {t } \times \mathbf { r } ^ {t t } \right| ^ { 2 } }$$
Find the torsion of the curve defined by $\mathbf { r } ( t ) = \cos 2 t \mathbf { i } + \sin 2 t \mathbf { j } + 5 t \mathbf { k }$ .

• A) \(\frac { 27 } { 29 }\)
• B) \(\frac { 10 } { 29 }\)
• C) \(\frac { 50 } { 29 }\)
• D) \(\frac { 7 } { 29 }\)

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Definitions:

Horney's Theory

A psychoanalytic theory by Karen Horney focusing on social and cultural factors affecting personality, introducing the concepts of basic anxiety and neurotic needs.

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Behavioral Evidence

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Social Cognitive Theory

A theory that emphasizes the importance of observational learning, imitation, and modeling in understanding behavior.