Let C₁ be the Rectangular Loop Consisting of Four Line

question 60

Multiple Choice

Let C₁ be the rectangular loop consisting of four line segments: from (0, 0) to (1, 0) , then to (1, 2) , then to (0, 2) , then back to (0, 0) .Suppose C₂ is the triangular loop joining (0, 0) to (1, 0) , then to (1, 2) then back to (0, 0) , and C₃ is another triangular loop joining (0, 0) to (1, 2) , then to (0, 2) and then back to (0, 0) . Is it true that $\int _ { c _ { 2 } } \vec { F } \cdot \overline { d r } = \int _ { C _ { 3 } } \vec { F } \cdot \overline { d r } + \int _ { C _ { 1 } } \vec { F } \cdot \overline { d r }$ for any vector field $\vec{F}$ defined on the xy-plane?

• A)Not possible to decide
• B)Yes
• C)No

---

Definitions:

Phoneme

The smallest unit of sound in a language that can distinguish one word from another, playing a critical role in phonetics and linguistics.

Basic Sound Unit

The smallest unit of sound in a language that can convey a distinct meaning, for example, a phoneme.

Natural Concept

A type of concept that is understood through everyday experiences and interactions with the world, unlike formal concepts that are defined by specific sets of rules or characteristics.

Cognition

The mental action or process of acquiring knowledge and understanding through thought, experience, and the senses.