Answer
a). magnitude of $F_{1}+F_{2}$ is possible.
This is possible when the two vectors are on the same line, and direction, the angle between them is zero.
b). magnitude of $F_{1}-F_{2}$ is possible.
This is possible when the two vectors are on the same line, but opposite direction, the angle between them is $180^{\circ}$.
c). magnitude of $\sqrt (F_{1}^{2} +F_{2}^{2})$ is possible.
This is possible, when the two vectors are perpendicular to each other. The angle between them is $90^{\circ}$.
Work Step by Step
a). magnitude of $F_{1}+F_{2}$ is possible.
This is possible when the two vectors are on the same line, and direction, the angle between them is zero.
b). magnitude of $F_{1}-F_{2}$ is possible.
This is possible when the two vectors are on the same line, but opposite direction, the angle between them is $180^{\circ}$.
c). magnitude of $\sqrt (F_{1}^{2} +F_{2}^{2})$ is possible.
This is possible, when the two vectors are perpendicular to each other. The angle between them is $90^{\circ}$.
