What are concurrent forces? Explain the equilibrium of a particle under the effect of concurrent forces.

(N/A) Concurrent forces: If the line of action of all given forces passes through the same point,then these forces are called concurrent forces.
In mechanics,when the resultant force acting on a particle is zero,the particle is said to be in equilibrium. In this case,the particle is either stationary or moving with a constant velocity.
If only one force $\vec{F}$ acts on a particle,it has accelerated motion and cannot remain in equilibrium.
If two forces $\vec{F}_{1}$ and $\vec{F}_{2}$ act on a particle,then for equilibrium,$\Sigma \vec{F} = 0$,which means:
$\vec{F}_{1} + \vec{F}_{2} = 0$
$\therefore \vec{F}_{1} = -\vec{F}_{2}$
If three forces $\vec{F}_{1}, \vec{F}_{2},$ and $\vec{F}_{3}$ act on a particle,then for equilibrium,$\Sigma \vec{F} = 0$:
$\vec{F}_{1} + \vec{F}_{2} + \vec{F}_{3} = 0$
$\therefore \vec{F}_{3} = -(\vec{F}_{1} + \vec{F}_{2})$
By the parallelogram law of forces,the resultant force of $\vec{F}_{1}$ and $\vec{F}_{2}$ is represented by the diagonal. When a force $\vec{F}_{3}$ of equal magnitude is applied in the opposite direction,the particle will be in equilibrium. By the triangle law of vectors:
$\vec{PQ} + \vec{QR} + \vec{RP} = 0$
$\therefore \vec{F}_{1} + \vec{F}_{2} + \vec{F}_{3} = 0$
$\therefore \Sigma \vec{F} = 0$