# Proof of vector circulation

1. Apr 25, 2013

### skate_nerd

1. The problem statement, all variables and given/known data

So a, b, and c are points in the plane. Let nab, nbc, and nca be vectors perpendicular to ab(vector), bc(vector), and ca(vector) respectively, and point towards the exterior of the triangle abc. Also, |nab|=|ab(vector)|, |nbc|=|bc(vector)|, and |nca|=|ca(vector)|. Show that nab+nbc+nca=0.

2. Relevant equations

I'm guessing that the formula for the dot product will be used, and that nab(dot)ab=0, and same for the other two vector combinations.

3. The attempt at a solution

Also, we have been learning about circulation integrals and line integrals. Not really sure if that proves much, but I know that the circulation around this triangle would be equal to 0 also, so there's something. Not sure really what else I have to go on though. I'm not very well versed in proofs, and my calc 3 teacher sure loves making us do them.

2. Apr 25, 2013

### dx

You know that

ab + bc + ca = 0

Now simply apply a rotation by 90 degrees