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

question 40

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 $\mathbf { T } ( t )$ and $\mathbf { N } ( t )$ 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:

Team-based Organization

A structural approach where work and processes are organized around groups rather than individual tasks or hierarchies.

Gig Economy

Workers who are involved in some form of freelancing, contracting, often based on outsourcing.

Virtual Teams

Groups of people who work together from different geographical locations, connected by technology such as email, video conferencing, and collaboration software.

E-leader

A leader who uses electronic means, such as email, social media, and virtual meeting platforms, to manage and guide teams, especially in remote or digital workplaces.