**Forces in Space (3D Forces)**

Magnitude of a force F in space

Components of a force in space

$F_y = F \cos \theta_y$

$F_z = F \cos \theta_z$

Direction cosines

$\cos \theta_y = \dfrac{F_y}{F}$

$\cos \theta_z = \dfrac{F_z}{F}$

Proportion of components

Moment of a force about an axis

$M_y = zF_x \pm xF_z$

$M_z = yF_x \pm xF_y$

**Resultant of Concurrent Force Systems in Space**

Components of the resultant

$R_y = \Sigma F_y$

$R_z = \Sigma F_z$

Magnitude of the resultant

**Equilibrium of Concurrent Space Forces**

The resultant of all forces is zero

$\Sigma F_y = 0$

$\Sigma F_z = 0$

The sum of moment is zero

$\Sigma M_y = 0$

$\Sigma M_z = 0$