When three forces acting upon a point are not coplanar, the resultant is the diagonal of the Parallelepiped of which the forces are sides.
Similar results are obtained for any number of forces.
Figure 5 : Let A B, A C, and A D be forces acting upon A. Their total resultant is A r .
Parallel Forces
When two parallel forces are applied at the extremities of a straight line, they have a resultant equal to their sum and acting at a point
which divides the straight line into parts inversely proportional to the forces.
Let A D and B E be two parallel forces acting upon the line AB.
Their resultant will be represented in direction and magnitude by CR.
AC : BE:: BC : AD
Figure 6: Resultant
Resultant Vector
When two forces are parallel but opposite in direction, their resultant will still be parallel to the components, but its magnitude will be equal to the difference of the components instead of the sum. The force will act at a point in a straight line dividing the line into segments inversely proportional to the forces.
