Let $C$ Be a Smooth Curve Defined By $\mathbf { r } ( t ) = 2 \mathbf { i } + 3 t \mathbf { j } + 2 t ^ { 2 } \mathbf { k }$

question 19

Multiple Choice

Let $C$ be a smooth curve defined by $\mathbf { r } ( t ) = 2 \mathbf { i } + 3 t \mathbf { j } + 2 t ^ { 2 } \mathbf { k }$ , and let $\mathrm { T } ( t )$ and $\mathrm { N } ( t )$ be the unit tangent vector and unit normal vector to $C$ corresponding to $t$ . The plane determined by $\mathbf { T }$ and $\mathbf { N }$ is called the osculating plane. Find an equation of the osculating plane of the curve described by $\mathbf { r } ( t )$ at $t = 1$ .

• A) \(z = 2\)
• B) \(y = 3\)
• C) \(2 x + 3 y + 2 z = 1\)
• D) \(x = 2\)

---

Definitions:

Underreport

The act of reporting less than the actual number or extent of something, often to conceal the true scale.

Freud's Theory

A set of psychoanalytic theories developed by Sigmund Freud, often focusing on unconscious desires and childhood experiences.

Unconscious Forces

Psychological factors that influence human behavior and decision-making without the individual's conscious awareness, a concept profound in psychoanalytic theory.

Libido

A term used to describe one's sexual drive or desire for sexual activity.