Answer
Figure A: the line integral of the vector field is positive
Figure B: the line integral of the vector field is positive
Figure C: the line integral of the vector field is positive
Work Step by Step
Figure A: the line integral of the vector field is positive
Explanation: the dot products ${\bf{F}}\cdot{\bf{T}}$ are positive along the path because the angle between the vectors are acute.
Figure B: the line integral of the vector field is positive
Explanation: most of the dot products ${\bf{F}}\cdot{\bf{T}}$ are positive along the path because the angle between the vectors are obtuse. Therefore, the line integral is positive.
Figure C: the line integral of the vector field is positive
Explanation: most of the dot products ${\bf{F}}\cdot{\bf{T}}$ are positive along the path because the angle between the vectors are acute. Though, there are some negative dot products closer to the end of the path, the positive values are dominant. Therefore, the line integral is positive.