Vector Analysis Basic Concepts
In this post, we will discuss about the basic concepts of vectors.
Scalars
Scalars are physical quantities, which are described completely by its magnitude and units.
Examples: Mass, length, time, density, energy, work, temperature, charge etc.
Note: Scalar can be added, subtracted and multiplied by the ordinary rule of algebra.
Vectors
Vectors are the physical quantities which are escribed completely by its magnitude, unit and its direction.
Examples: Force, velocity, acceleration, momentum, torque, electric field and magnetic field forces etc.
Note: Vectors are added, subtracted, multiplied by using vector algebra.
Representation of vector
A vector quantity is represented by two ways.
1. Symbolically
2. Graphically
1. Symbolical representation:
A vector quantity is represented by a bold letter such as F. a, d.
OR
It is represented by a bar or an arrow over their symbols. Such as 
2-Graphically representation:
A vector can be represented by a line segment with an arrow head as shown in figure.
The line AB with arrow head at B represent a vector v. The length of line AB gives the magnitude of vector V on a selected scale. While the direction of the line A to B gives the direction of vector V.
Position vector
A vector, whose initial point is origin O and terminal point is P, is called position vector and it is written as OP.
Position Vector representation in two and three dimensional coordinate system:
Let R be set of real numbers. In the Cartesian plane
position vector is written as 
In three dimensional coordinate system
position vector written as 
Magnitude ( length or norm)
Magnitude of a vector OP is its absolute value and it is written as
Null or zero vector
A vector having zero magnitude is called Null or zero vectors.
Unit vector
A vector having unit magnitude and having direction along the given vector is called unit vector. These are usually represented by รข. If we consider a vector A , then its unit vector can be written as
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