Line integral conceptual help

1. Mar 4, 2008

EngageEngage

1. The problem statement, all variables and given/known data
If the vector field F(x,y,z) is everywhere parallel to R and C is a curve drawn on a sphere with the center at the origin, then:
$$\int$$$$\stackrel{C}{}$$ F . dR = 0
why?
3. The attempt at a solution

Im not exactly sure if I understand the problem, but this is the explanation i came up with: If R is the position vector of the curve (which lies on a sphere), and vector field F lies parallel to R we know that F will be perpendicular everywhere to C, thus satisfying this condition... is this right? is R the position vector in this case (i'm somewhat confused because the book i'm using is somewhat inconsistent with notation). If someone could please tell me if i'm doing this right that would be greatly appreciated.