Answer
Figure A: the line integral of the vector field is zero
Figure B: the line integral of the vector field is negative
Figure C: the line integral of the vector field is zero
Work Step by Step
Figure A: the line integral of the vector field is zero
Explanation: the dot products ${\bf{F}}\cdot{\bf{T}}$ are negative on the upper half of the circle because the angle between the vectors are obtuse. However, the dot products ${\bf{F}}\cdot{\bf{T}}$ are positive on the lower half of the circle because the angle between the vectors are acute. Since ${\bf{F}}$ is the same on both halves, the dot products cancel out. Hence, total line integral is zero.
Figure B: the line integral of the vector field is negative
Explanation: the dot products ${\bf{F}}\cdot{\bf{T}}$ are negative on the upper half of the circle because the angle between the vectors are obtuse. However, the dot products ${\bf{F}}\cdot{\bf{T}}$ are positive on the lower half of the circle because the angle between the vectors are acute. Since ${\bf{F}}$ is stronger at the upper half, total line integral is negative.
Figure C: the line integral of the vector field is zero
Explanation: the dot products ${\bf{F}}\cdot{\bf{T}}$ are zero since the angle between the vectors are $90^\circ $ along the circle.