Triangle Law, Parallelogram Law and Polygon Law of Vectors.

1. Triangle Law of Vectors :

If two vectors can be represented both in magnitude and direction by the sides of a taken in the same order, then their resultant is represented completely in magnitude and direction, by the third side of the triangle taken in the opposite order. Shown in fig.

Resultant vector(R) is equal to sum of two vectors(P,Q). Relation is

Case : If three vectors are represented by all three sides of a triangle taken in same order then their resultant is zero. Shown in fig.

And that has relation is 

2. Parallelogram Law of Forces :

If two forces acting simultaneously on a body can be represented completely (in magnitude and direction) by the two adjacent sides of a parallelogram drawn from a point then their resultant is represented completely (in magnitude and direction) by the diagonal of the parallelogram passing through the same point of intersection. Shown in fig.

The magnitude of resultant force is

Direction of resultant force is

3. Polygon Law of Forces :

According to this law if a number of forces can be represented in magnitude and direction by the sides of an open polygon taken in same order, then their resultant is represented in magnitude and direction by the closing side of the polygon taken in opposite order. Shown in fig. 

According to this law, resultant vector is equal to sum of all vectors. And it has relation is