TRIANGLE LAW OF FORCES

TRIANGLE LAW OF FORCES
CONCEPT
Consider a body, on which, forces P and Q are acting. Note that the forces P and Q are acting in an order. That is, order in which P & Q act, lead to anticlockwise rotation. Let AB represent force P. The length of AB represents the magnitude of P, that is, if P is 4N, then the length of AB is 4cm, 4inches or any other value proportional to 4N depending on the scale you choose. The arrow mark on AB represents the direction of P. Similarly, let BC represent force Q, in magnitude, and direction. You can see that AB and BC represent two sides of a triangle. If we complete the triangle, by drawing the third side CA, it represents the resultant force of P and Q. Lets call it R. Note that, the direction of R is in the clockwise direction, which is opposite to the direction of P & Q. This is what is called, the Triangle law of forces.
STATEMENT
The law states that "If two forces, acting on a body, are represented in magnitude and direction by two sides of a triangle taken in order, then, the resultant of the two forces is represented in magnitude and direction by the third side of the triangle, taken in the opposite order.
EXPLANATION
Lets look at this statement part by part:
"If two forces, acting on a body ..." This talks about the two forces P and Q that act on the body.
Okay lets look at the next part of the statement. "represented in magnitude and direction by two sides of a triangle". In triangle ABC, side AB and side BC represent the forces P & Q in magnitude, as well as in direction.
"taken in order,". Order in which P & Q act, lead to anticlockwise rotation.
"then the resultant of the two forces is represented in magnitude and direction by the third side of the triangle,". The third side of the triangle, that is AC, represents the resultant of P & Q in magnitude and direction.
"taken in the opposite order". That is, the direction of R is opposite to P & Q.
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[GE6253 - ENGINEERING MECHANICS - BASICS AND STATICS OF PARTICLES]

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