Answer to Question #169250 in Physics for Maisie

Question

If three concurrent forces are in equilibrium, what is the relation between any one of the three forces and the resultant of the other two forces?

Answer 1

Let $\mathbf{F}_1, \mathbf{F}_2, \mathbf{F}_3$ be three concurrent forces (bold denotes vectors). Since the body is in equilibrium, the following equation should hold:

$$\mathbf{F}_1+ \mathbf{F}_2+ \mathbf{F}_3 = 0$$

Let $\mathbf{F}_{23}$ also be the resultant of forces $\mathbf{F}_2$ and $\mathbf{F}_3$: $\mathbf{F}_{23} = \mathbf{F}_2+\mathbf{F}_3$. Then obtain:

$$\mathbf{F}_1 + \mathbf{F}_{23} = 0\\ \mathbf{F}_1 = -\mathbf{F}_{23}$$

Thus, one of the three forces should have equal magnitude and opposite direction with the resultant of the other two forces.

Answer. Equal mabnitudes and opposite directions.