Find the Unit Tangent and Unit Normal Vectors $\mathrm { T } ( t )$

question 159

Essay

Find the unit tangent and unit normal vectors $\mathrm { T } ( t )$ and $\mathrm { N } ( t )$ for the curve $C$ defined by $\mathbf { r } ( t ) = t \mathbf { i } + 2 t ^ { 2 } \mathbf { j }$ . Sketch the graph of $C$ , and show $\mathbf { T } ( t )$ and $N ( t )$ for $t = 1$ .

---

Definitions:

Objective Standard

A universal, unbiased criterion used to evaluate actions, situations, or decisions, not influenced by personal feelings or opinions.

Subjective Test

An assessment criteria based on personal opinions, feelings, and perspectives, rather than objective, measurable standards.

Material Breach

A significant failure to perform one's contractual obligations, which justifies the other party's termination of the contract.

Basic Principles

Fundamental rules or doctrines that form the foundation for a system of belief, behavior, or reasoning.