Condition Of Equilibrium

When forces are in equilibrium, that is, there is no net force and the summation of the particle's moment, taken at any point, is equal to 0.

$\sum F_{x} = 0$

$\sum F_{y} = 0$

$\sum F_{z} = 0$

$\sum M_{o} = 0$

Newton's Second Law of Motion

$F = m a$

$\frac{a}{s i n A} = \frac{b}{s i n B} = \frac{c}{s i n C}$

$a^{2} = b^{2} + c^{2} - 2 b c \cos A$

$b^{2} = a^{2} + c^{2} - 2 a c \cos B$

$c^{2} = a^{2} + b^{2} - 2 a b \cos C$

$\vec{a} ∙ \vec{b} = a b \cos θ$

\vec{a} \times \vec{b} = (\begin{matrix} a_{1} \\ a_{2} \\ a_{3} \end{matrix}) \times (\begin{matrix} b_{1} \\ b_{2} \\ b_{3} \end{matrix}) = (\begin{matrix} a_{2} b_{3} - a_{3} b_{2} \\ a_{3} b_{1} - a_{1} b_{3} \\ a_{1} b_{2} - a_{2} b_{1} \end{matrix}) = | \vec{a} | | \vec{b} | \sin (θ) \cdot \vec{e}