Latest revision as of 14:11, 4 January 2018

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.

$\sum F_{x} = 0$

$\sum F_{y} = 0$

$\sum F_{z} = 0$

$\sum M_{o} = 0$

$F = m a$

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

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

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

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

$\vec{a} ∙ \vec{b} = a b \cos θ$

\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}