Lami's Theorem

Theorem
Let $B$ be a body in static equilibrium.

Let the only forces acting on $B$ be $F_a$, $F_b$ and $F_c$.

Let $F_a$, $F_b$ and $F_c$ be represented by the vectors $V_a$, $V_b$ and $V_c$ respectively, such that the magnitudes and directions of each force corresponds to the magnitudes and directions of each vectors.

Let the directions of $V_a$, $V_b$ and $V_c$ be non-parallel.

Then $V_a$, $V_b$ and $V_c$ are coplanar and concurrent, and:


 * $\dfrac {\size V_a} {\sin A} = \dfrac {\size V_b} {\sin B} = \dfrac {\size V_c} {\sin C}$

where:
 * $A$, $B$ and $C$ are the angles between the directions of $V_b$ and $V_c$, $V_a$ and $V_c$, and $V_a$ and $V_b$ respectively
 * $\size V_a$, $\size V_b$ and $\size V_c$ are the magnitudes of $V_a$, $V_b$ and $V_c$ respectively.