Scalars And Vectors

Polygon Law of Vectors

Polygon law of vectors states that if a particle simultaneously possesses a number of vectors which are represented in magnitude and direction by the sides of a polygon taken in order, then their resultant vector is represented both in magnitude and direction by the closing side of the polygon taken in opposite order.

Consider a particle O which possesses vectors u, v, w, x and y simultaneously.

Draw a vector AB parallel and equal to u such that AB represents the vector u of the particle both in magnitude and direction. Similarly, represent the magnitude and direction of the vectors v, w, x and y by BC, CD, DE and EF respectively.

Polygon Law of Vectors

Now, join AF. Then, the resultant z of the vectors u, v, w, x and y is represented in magnitude and direction by the vector AF, the closing side of the polygon.

AF=AB+BC+CD+DE+EF

or,z=u+v+w+x+y

If the particle possesses a number of vectors which can be represented in magnitude and direction by the sides of a closed polygon taken in order then the particle is in equilibrium state.

Represent the vectors u, v, w, x, y and z of the particle O in magnitude and direction by the sides AB, BC, CD, DE, EF and FA of the closed polygon ABCDEF.

Polygon Law of Vectors: Equilibrium State

We know that the resultant of u, v, w, x and y must have the same magnitude but opposite direction as that of z.

u+v+w+x+y+z

=z+z=0

Hence, the result of u, v, w, x, y and z will be zero and the particle will be in equilibrium state.