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 a lot here.