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Mathematical concept of vector is basically secular in nature and general in application. This means that mathematical treatment of vectors is without reference to any specific physical quantity or phenomena. In other words, we can employ vector and its methods to all quantities, which possess directional attribute, in a uniform and consistent manner. For example two vectors would be added in accordance with vector addition rule irrespective of whether vectors involved represent displacement, force, torque or some other vector quantities.

The moot point of discussion here is that vector has been devised to suit the requirement of natural process and not the other way around that natural process suits vector construct as defined in vector mathematics.

What is a vector?

Vector
Vector is a physical quantity, which has both magnitude and direction.

A vector is represented graphically by an arrow drawn on a scale as shown Figure i . In order to process vectors using graphical methods, we need to draw all vectors on the same scale. The arrow head point in the direction of the vector.

A vector is notionally represented in a characteristic style. It is denoted as bold face type like “ a ” as shown Figure (i) or with a small arrow over the symbol like “ a ” or with a small bar as in “ a - ”. The magnitude of a vector quantity is referred by simple identifier like “a” or as the absolute value of the vector as “ | a | ” .

Two vectors of equal magnitude and direction are equal vectors ( Figure (ii) ). As such, a vector can be laterally shifted as long as its direction remains same ( Figure (ii) ). Also, vectors can be shifted along its line of application represented by dotted line ( Figure (iii) ). The flexibility by virtue of shifting vector allows a great deal of ease in determining vector’s interaction with other scalar or vector quantities.

Vectors

It should be noted that graphical representation of vector is independent of the origin or axes of coordinate system except for few vectors like position vector (called localized vector), which is tied to the origin or a reference point by definition. With the exception of localized vector, a change in origin or orientation of axes or both does not affect vectors and vector operations like addition or multiplication (see figure below).

Vectors

The vector is not affected, when the coordinate is rotated or displaced as shown in the figure above. Both the orientation and positioning of origin i.e reference point do not alter the vector representation. It remains what it is. This feature of vector operation is an added value as the study of physics in terms of vectors is simplified, being independent of the choice of coordinate system in a given reference.

Vector algebra

Graphical method is slightly meticulous and error prone as it involves drawing of vectors on scale and measurement of angles. In addition, it does not allow algebraic manipulation that otherwise would give a simple solution as in the case of scalar algebra. We can, however, extend algebraic techniques to vectors, provided vectors are represented on a rectangular coordinate system. The representation of a vector on a coordinate system uses the concept of unit vectors and scalar magnitudes. We shall discuss these aspects in a separate module titled Components of a vector . Here, we briefly describe the concept of unit vector and technique to represent a vector in a particular direction.

Questions & Answers

A stone propelled from a catapult with a speed of 50ms-1 attains a height of 100m. Calculate the time of flight, calculate the angle of projection, calculate the range attained
Samson Reply
water boil at 100 and why
isaac Reply
what is upper limit of speed
Riya Reply
what temperature is 0 k
Riya
0k is the lower limit of the themordynamic scale which is equalt to -273 In celcius scale
Mustapha
How MKS system is the subset of SI system?
Clash Reply
which colour has the shortest wavelength in the white light spectrum
Mustapha Reply
how do we add
Jennifer Reply
if x=a-b, a=5.8cm b=3.22 cm find percentage error in x
Abhyanshu Reply
x=5.8-3.22 x=2.58
sajjad
what is the definition of resolution of forces
Atinuke Reply
what is energy?
James Reply
Ability of doing work is called energy energy neither be create nor destryoed but change in one form to an other form
Abdul
motion
Mustapha
highlights of atomic physics
Benjamin
can anyone tell who founded equations of motion !?
Ztechy Reply
n=a+b/T² find the linear express
Donsmart Reply
أوك
عباس
Quiklyyy
Sultan Reply
Moment of inertia of a bar in terms of perpendicular axis theorem
Sultan Reply
How should i know when to add/subtract the velocities and when to use the Pythagoras theorem?
Yara Reply
Centre of mass of two uniform rods of same length but made of different materials and kept at L-shape meeting point is origin of coordinate
Rama Reply

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Source:  OpenStax, Physics for k-12. OpenStax CNX. Sep 07, 2009 Download for free at http://cnx.org/content/col10322/1.175
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