If R(t) Is the Position Vector of a Particle in the Plane

question 68

Multiple Choice

If r(t) is the position vector of a particle in the plane at time t, find the indicated vector.
-Find the velocity vector. r(t) = (cot t) i + (csc t) j

• A) \(\mathbf { v } = \left( - \sec ^ { 2 } t \right) \mathbf { i } - ( \tan t \sec t ) \mathbf { j }\)
• B) \(\mathbf { v } = \left( \csc ^ { 2 } \mathrm { t } \right) \mathbf { i } + ( \cot \mathrm { t } \csc \mathrm { t } ) \mathbf { j }\)
• C) \(\mathbf { v } = \left( - \csc ^ { 2 } \mathrm { t } \right) \mathbf { i } - ( \cot \mathrm { t } \csc \mathrm { t } ) \mathbf { j }\)
• D) \(\mathbf { v } = \left( \sec ^ { 2 } \mathrm { t } \right) \mathbf { i } + ( \tan \mathrm { t } \sec \mathrm { t } ) \mathbf { j }\)

---

Definitions:

Dissonance

A psychological state of conflict or uneasiness resulting from conflicting beliefs, attitudes, or behaviors.

High-Level Wellness

A state of complete physical, mental, and social well-being, and not merely the absence of disease or infirmity.

Integrated Method

A comprehensive approach that combines various methods or techniques to achieve enhanced outcomes or solve complex problems.

Continuum of Balance

Refers to the dynamic range or spectrum over which something, like a psychological state or physical condition, can vary between two polar opposites or extremes.