Conditions of equilibrium for forces in space are as follows:-

(i)The total force acting on an object is 0

a) The total horizontal force acting on an object is 0

$ i.e\space \space \sum F_x=0$

Consider a beam,

Then according to the condition of equilibrium,

$\sum F_x=0 \\ \therefore \sum F_a \cos α-F_b \cos β=0$

b) The total vertical force acting on an object is 0

$$i.e. \sum F_y=0$$

Consider the same example as above. According to the condition of equilibrium, $\sum F_y=0 \\ \therefore R_1+R_2-F_a \sin α-F_b \sin β=0 $

(ii)The total torque or moment acting on an object about any point is 0.

$i.e. \sum M=0$

Consider the same example, Taking moment about point A, according to this condition, we get,

$\sum M_A=0 \\ \therefore -(F_B \sin β).x+R.L=0$