Expalin how to find addition of vectors and subtration of vectors, also give the situation from everyday life.

Vectors are quantities having both magnitude and direction. 

 

ADDITION OF VECTORS.

They cannot be added by the simple laws of addition liike scalars.A vector can be added to another vector of same nature only.

1. When two vectors act in the same direction:

 

Consider a car moving 3 m due east and then 3 m again due east .If the two displacement vectors are represented by   ,then the sum ()of the two displacement vectors will be displacement 6 m due east.

2.When two vectors act in the opposite diection:

 

Consider a case when a man walks through 5 m due east and then through 3 m due west. then the sum() of the two displacement vectors will be a displacemnt of 2 m due east.

3. When two vectors are inclined at right angles to each other:

 

Suppose a particle is first displaced through 5m due east and then through 2 m due north and is represented by vectors .The resultant displacement is given as :

The resultant of two or more vectors is a single vector which produces the same effect as the individual vectors produce together.

Vectors cannot be added algebraically but they are added according to the law of vector addition.

There are three laws of vector addition:

1. Triangle law of vector addition

2. Parrallelogram law of vector addition

3. Polygon law of vector addition

 

SUBTRACTION OF VECTORS

 

The subtraction of a vector  from vector  is defined as the addition of vector 

In everyday life when you have to calculate both magnitude and direction of a parameter we use vectors like to find the speed and direction of moving objects such as cars boat, airplanes, wind speed.

Two find the relative speed of one moving object with respect to other.We can find the speed and direction of rain falling vertically downwards using vectors.Using vectors we can determine the speed and direction in sail boats etc.