Find the Principal Unit Normal Vector N for the Curve $$\mathbf { r } ( t ) = ( 10 + t ) \mathbf { i } + ( 9 + \ln ( \cos t ) ) \mathbf { k } , - \pi / 2 < t < \pi / 2$$

question 2

Multiple Choice

Find the principal unit normal vector N for the curve r(t) .
- $$\mathbf { r } ( t ) = ( 10 + t ) \mathbf { i } + ( 9 + \ln ( \cos t ) ) \mathbf { k } , - \pi / 2 < t < \pi / 2$$

• A) N = (-cos t)i - (ln(cos t))k
• B) N = (cos t)i + (sin t)k
• C) N = (-sin t)i - (cos t)k
• D) N = (-cos t)i - (tan t)k

---

Definitions:

Cognitive-Affective Personality System (CAPS)

A theory that emphasizes the importance of situational variables and cognitive processes in understanding personality.

Cognitive-Affective Personality System (CAPS)

A psychological theory that emphasizes the interaction of cognitive and emotional processes in shaping personality.

Personality System

The organized set of characteristics, traits, and behaviors that uniquely define how a person interacts with the environment and others.

Insight

The ability to understand the inner nature of things or a deep understanding of a person or situation.