13.2 #4

I am a bit confused about this question. I know that the middle one (the
one at the top, perpendicular to the vector field) has its integral, and
therefore work, equal to zero. However, the other two don't make sense. The
one traveling in the direction of the vector field should be positive,
right?

The vector field is in the same direction as the path, so that
equates to a positive line integral? If that is the case, why is it the
smallest? Am I just confused?

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The one traveling in the same direction of the vector field, C3, will have dr parallel to F, hence F.dr is positive, hence the integral will be positive (this is greater than the integral over C1, which is zero). On the other hand integrating over C2, dr will be in the opposite direction as F, hence F.dr is negative hence so is the integral over C2.