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

question 77

Multiple Choice

The torsion of a curve defined by $\mathbf { r } ( t )$ is given by $\tau = \frac { \left( \mathbf { r } ^ { t } \times \mathbf { r } ^ { \prime \prime } \right) \cdot \mathbf { r } ^ { m \prime } } { \left| \mathbf { r } ^ { t } \times \mathbf { r } ^ { \prime t } \right| ^ { 2 } }$ 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) \(\frac { 7 } { 29 }\)

---

Definitions:

Illusory Correlation

The belief in a connection between two factors when in reality, there is no such link.

Express Checkout

A dedicated checkout lane in stores for customers purchasing a limited number of items, designed for quick service.

Actor-Observer Bias

A cognitive bias that involves attributing one's own actions to external factors while attributing others' actions to their character or personality.

Self-Serving Bias

A cognitive bias where people attribute positive outcomes to their own actions and negative outcomes to external factors.