Vectors
1.0 Introduction
2.0 Types of Vectors
3.0 Addition of Vectors
4.0 Components of a Vector
5.0 Vector Joining Two Points
6.0 Projection of a Vector on a Line
7.0 Section Formula
8.0 Products of a Vector
9.0 Lami's Theorem
10.0 Linear Combination of Vectors
11.0 Linearly Dependent and Independent Vectors
12.0 Scalar Triple Product
13.0 Vector Triple Product
3.1 Parallelogram Law of Vector Addition
Consider two vectors $\overrightarrow p $ and $\overrightarrow q $, representing the two adjacent sides of a parallelogram in magnitude and direction as shown in figure, then their sum $\overrightarrow p + \overrightarrow q $ is represented in magnitude and direction by the diagonal of the parallelogram through their common point. This is known as the parallelogram law of vector addition.
From the figure, one may write as $$\overrightarrow {OP} = \overrightarrow {PR} + \overrightarrow {OR} $$
or it can be written as $$\overrightarrow {OP} = \overrightarrow {OQ} + \overrightarrow {OR} $$Since,$$\overrightarrow {PR} = \overrightarrow {OQ} $$
So, we can conclude that traiangle law and parallelogram law of vector addition are equivalent to each other.
