# Statics/Three-Dimensional Equilibrium

There are six equations expressing the equilibrium of a rigid body in 3 dimensions.

Sum of Forces: $\sum_{}^{} F_x=0$, $\sum_{}^{} F_y=0$, $\sum_{}^{} F_z=0$

Sum of Moments: $\sum_{}^{} M_x=0$, $\sum_{}^{} M_y=0$, $\sum_{}^{} M_z=0$

To solve three dimensional statics problems:

• Resolve force components
• Resolve moments about a point
• Resolve moments about a line or axis. See Scalar Triple Product

Knowing how to find the Determinate of a matrix can help alot here.