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Let $\mathbf F_1, \mathbf F_2, \ldots, \mathbf F_n$ be a set of $n$ forces acting on a particle $B$ at a point $P$ in space.

The equilibrant of $\mathbf F_1, \mathbf F_2, \ldots, \mathbf F_n$ is defined as the force which is needed to prevent $B$ from moving.


Forces at $\polar {100 \, \mathrm {kg}, 150 \degrees}, \polar {75 \, \mathrm {kg}, 60 \degrees}, \polar {50 \, \mathrm {kg}, -45 \degrees}$

Three forces $\mathbf F_1, \mathbf F_2, \mathbf F_3$ act on a particle $B$ at a point $P$ embedded in the complex plane:

\(\ds \mathbf F_1\) \(=\) \(\ds \polar {100 \, \mathrm {kg}, 150 \degrees}\)
\(\ds \mathbf F_2\) \(=\) \(\ds \polar {75 \, \mathrm {kg}, 60 \degrees}\)
\(\ds \mathbf F_3\) \(=\) \(\ds \polar {50 \, \mathrm {kg}, -45 \degrees}\)

Equilibrant-100kg at 150, 75kg at 60, 50kg at -45.png

The equilibrant $\mathbf E$ of $\mathbf F_1, \mathbf F_2, \mathbf F_3$ is:

$\mathbf E = \polar {80.8 \, \mathrm {kg}, -80.2 \degrees}$

Also see