Introduction of Vector Algebra

Algebra Of Vectors - Introduction

Physical quantities are divided in to two categories - Scalar quantities and Vector quantities.

Scalar - Quantities having magnitude only are know as Scalars. e.g. Length, Mass, Time etc.

Vectors - The quantities specified by magnitude and direction both are called vectors. e.g. Force, Velocity, Acceleration, Weight.

NOTE - It is to note here that in addition to magnitude and direction, two vector quantities of the same kind should be capable of being compounded according to parallelogram law of addition. Quantities having magnitude and direction but not obeying the parallelogram law of addition will not be treated as vectors.

For example - The rotations of a rigid body through finite angles have both magnitude and direction but do not satisfy the parallelogram law of addition.

Representation of Vectors.

A vector is denoted by $\overrightarrow{AB}$ is determined by two points A and B
Magnitude of the the vector is the length of line AB and its direction by an arrow sign on line AB.

                    where Point A → initial point of vector $\overrightarrow{AB}$
                    where Point B → terminal point of vector $\overrightarrow{AB}$

Vectors are generally denoted by $\overrightarrow{a}$ , $\overrightarrow{b}$, $\overrightarrow{c}$

A Vector has 

i) A magnitude ( length, modulus or module) - The length is called the magnitude of a vector written as 〡$\overrightarrow{AB}$〡

ii) A direction (sense) - Direction $\overrightarrow{AB}$ is A to B

iii) A support - The support of $\overrightarrow{AB}$ is the line of which $\overrightarrow{AB}$ is a part.