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

question 56

Multiple Choice

The torsion of a curve defined by $\mathbf { r } ( t )$ is given by
$$\tau = \frac { \left( \mathbf { r } ^ { t } \times \mathbf { r } ^ { tt } \right) \cdot \mathbf { r } ^ { ttt } } { \left| \mathbf { r } ^ { t } \times \mathbf { r } ^ { tt } \right| ^ { 2 } }$$
Find the torsion of the curve defined by $\mathbf { r } ( t ) = \cos 5 t \mathbf { i } + \sin 5 t \mathbf { j } + 4 t \mathbf { k }$ .

• A) \(\frac { 21 } { 41 }\)
• B) \(\frac { 9 } { 41 }\)
• C) \(\frac { 20 } { 41 }\)
• D) \(\frac { 80 } { 41 }\)

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Definitions:

Preconventional Moral Reasoning

The first level of Kohlberg's stages of moral development, where an individual's moral reasoning is based on external consequences rather than internalized standards.

Conventional Moral Reasoning

A stage of moral development where individuals make decisions based on societal norms and the expectations of others.

Distributive Justice

The ethical principle concerning the fair allocation of resources and goods in a society.

Conventional Moral Reasoning

A phase in the evolution of moral understanding where people base their decisions on the norms of society and what other people anticipate from them.