(a) Consider the line integral I = The integral of Fdr along the curve C
i) Suppose that the length of the path C is L. What is the value of I if the vector field F is normal to C at every point of C?
ii) What is the value of I if the vector field F is is a unit vector pointing in the negative direction along the curve at every point of C?
Integral of Fdr along c is F(r(t)) * r'(t)
The Attempt at a Solution
I understand the process of computing a line integral, but am unsure of these two parts.
I know for i) that a vector times its normal vector is 0, but F isn't r, it is a vector field of r.
For ii) I'm not even sure as to how to proceed. I do not know what my F(r(t)) would be nor my r'(t)