Let C₁ be the Rectangular Loop Consisting of Four Line

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