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.

${\displaystyle \sum F_{x}=0}$

${\displaystyle \sum F_{y}=0}$

${\displaystyle \sum F_{z}=0}$

${\displaystyle \sum M_{o}=0}$

Newton's Second Law of Motion

${\displaystyle F=ma}$

Trigonometry

Sine Law

${\displaystyle {a \over sinA}={b \over sinB}={c \over sinC}}$

Cosine Law

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

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

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

Vector Relations

Dot Product

${\displaystyle {\vec {a}}\bullet {\vec {b}}=ab\cos \theta }$

Cross Product

${\displaystyle {\vec {a}}\times {\vec {b}}={\begin{pmatrix}a_{1}\\a_{2}\\a_{3}\end{pmatrix}}\times {\begin{pmatrix}b_{1}\\b_{2}\\b_{3}\end{pmatrix}}={\begin{pmatrix}a_{2}b_{3}-a_{3}b_{2}\\a_{3}b_{1}-a_{1}b_{3}\\a_{1}b_{2}-a_{2}b_{1}\end{pmatrix}}=\left|{\vec {a}}\right|\left|{\vec {b}}\right|\sin(\theta )\cdot {\vec {e}}}$