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Vector addition represents the net effect of the directional quantties.

Vectors operate with other scalar or vector quantities in a particular manner. Unlike scalar algebraic operation, vector operation draws on graphical representation to incorporate directional aspect.

Vector addition is, however, limited to vectors only. We can not add a vector (a directional quantity) to a scalar (a non-directional quantity). Further, vector addition is dealt in three conceptually equivalent ways :

  • graphical methods
  • analytical methods
  • algebraic methods

In this module, we shall discuss first two methods. Third algebraic method will be discussed in a separate module titled Components of a vector

The resulting vector after addition is termed as sum or resultant vector. The resultant vector corresponds to the “resultant” or “net” effect of a physical quantities having directional attributes. The effect of a force system on a body, for example, is determined by the resultant force acting on it. The idea of resultant force, in this case, reflects that the resulting force (vector) has the same effect on the body as that of the forces (vectors), which are added.

Resultant force

It is important to emphasize here that vector rule of addition (graphical or algebraic) do not distinguish between vector types (whether displacement or acceleration vector). This means that the rule of vector addition is general for all vector types.

It should be clearly understood that though rule of vector addition is general, which is applicable to all vector types in same manner, but vectors being added should be like vectors only. It is expected also. The requirement is similar to scalar algebra where 2 plus 3 is always 5, but we need to add similar quantity like 2 meters plus 3 meters is 5 meters. But, we can not add, for example, distance and temperature.

Vector addition : graphical method

Let us examine the example of displacement of a person in two different directions. The two displacement vectors, perpendicular to each other, are added to give the “resultant” vector. In this case, the closing side of the right triangle represents the sum (i.e. resultant) of individual displacements AB and BC .


AC = AB + BC

The method used to determine the sum in this particular case (in which, the closing side of the triangle represents the sum of the vectors in both magnitude and direction) forms the basic consideration for various rules dedicated to implement vector addition.

Triangle law

In most of the situations, we are involved with the addition of two vector quantities. Triangle law of vector addition is appropriate to deal with such situation.

Triangle law of vector addition
If two vectors are represented by two sides of a triangle in sequence, then third closing side of the triangle, in the opposite direction of the sequence, represents the sum (or resultant) of the two vectors in both magnitude and direction.

Here, the term “sequence” means that the vectors are placed such that tail of a vector begins at the arrow head of the vector placed before it.

Questions & Answers

List the application of projectile
Luther Reply
How can we take advantage of our knowledge about motion?
Kenneth Reply
pls explain what is dimension of 1in length and -1 in time ,what's is there difference between them
Mercy Reply
what are scalars
Abdhool Reply
show that 1w= 10^7ergs^-1
Lawrence Reply
what's lamin's theorems and it's mathematics representative
Yusuf Reply
if the wavelength is double,what is the frequency of the wave
Ekanem Reply
What are the system of units
Jonah Reply
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
58asagravitasnal firce
water boil at 100 and why
isaac Reply
what is upper limit of speed
Riya Reply
what temperature is 0 k
0k is the lower limit of the themordynamic scale which is equalt to -273 In celcius scale
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

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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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