# What are the parallelogram and the polygon methods?

Mar 19, 2016

Parallelogram method is a method for finding sum or resultant of two vectors.
The polygon method is a method for finding sum or resultant of more than two vectors. (Can be used for two vectors also).

#### Explanation:

Parallelogram method

In this method, two vectors $\vec{u} \mathmr{and} \vec{v}$ are moved to a common point and drawn to represent two sides of a parallelogram, as shown in the picture. Diagonal of the parallelogram represents sum or resultant of the $\vec{u} + \vec{v}$

Polygon method

In polygon method of finding the sum or resultant of vectors $\vec{P} , \vec{Q} ,$
$\vec{R} , \vec{S} , \vec{T}$, are vectors are drawn from head to tail to form an open polygon, as shown. The starting point A is arbitrary. The resultant vector $\vec{R}$ is drawn from the tail of first vector to head of the last vector.
it may so happen that head of the last may end at the tail of first vector, resulting in a closed polygon. In such a case $\vec{R} = 0$ or it is called null vector.