[6.2] - Visualizing Vector Line Integrals


Answers
  1. The vector field, $\myv F$ has vector components along the path $C1$ in the same direction as the direction of integration, $\Rightarrow \int_{C1}\myv F\cdot d\myv r$ is positive.
  2. The vector field, $\myv F$ has vector components along the path $C1$ in the opposite direction as the direction of integration, $\Rightarrow \int_{C2}\myv F\cdot d\myv r$ is negative.
  3. No this is not a conservative field.
    If it were, the integral around any closed path, including $\oint_{C2}\myv F\cdot d\myv r$ would = 0. But in part b) we found that it was negative.