**RESULTANT OF TWO COPLANAR PARALLEL FORCES**

**3.5.1 Resultant of Two Like Coplanar Parallel Forces**

F1 and F2 are two like parallel forces, their resultant R = F1 + F2. Applying Varignon’s principle, we have

Or -F_{1} x AO +F_{2} x BO =R X CO =(F_{1}+F_{2}) CO

Or -F_{1} X AO +F_{2} X BO =F_{1} X CO +F_{2} X CO

Or F_{1} X (AO+CO) = F _{2} (BO-CO)

Or F_{1} X AC =F_{2} X BC

Or F_{1}/F_{2} =BC/AC, Thus point C is located

C is the point through which the resultant acts.

**3.5.2 Resultant of Two Coplanar Unlike Parallel Forces**

Applying the principle of moments about we get

O- F _{l} X AO – F _{2} X BO = -R X CO

= -R X CO

= – (F_{1}-F_{2}) CO

-F_{1} X AO –F_{2} X BO = – F_{1} XCO +CO +F_{2} X CO

F_{1} (CO –AO)

=F_{2} (BO+CO)

F_{1} X AC =F= X BC

F_{1} /F_{2} =BC/AC . This point C which is the application point of resultant is fixed.