Is this 2-plane vector field just an arbitrary plane embedded in R^3?
Could some offer an example of finding the line integral of a circle’s arc which is not centered at the origin and which passes through a simple 2-plane vector field?
I am having trouble parameterizing a circle’s path into terms of sine and cosine.
Thanks in advance.
I don't believe you are asking about a general plane in 3 dimensions. I interpret your question as just about integrating u(x,y)i+ v(x, y)j about an arbitrary circle, or arc of a circle, with center at some point other than (0, 0). That's much easier!
A circle, with radius R, with center at is given by and standard parametric equations , .