### Chapter : Vector

__Representation of Vector__

__Representation of Vector__

**2. Representation of Vector**

There are two methods for representation of vectors.

**(a) Graphical method.**

**(b) Mathematical method.**

**(a) Graphical method :**

The length of the arrow shows the magnitude and head of the arrow shows the direction.

**(b) Mathematical Representation :**

**(i) In the form of components :**If a

_{x}is a component of any vector in x-direction, a

_{y}is a component in y-direction and azis component in z-direction then

where a

_{x}, a

_{y}, a

_{z}may be the co-ordinates of point a.

**(ii)**

**Unit vector method :**If we want to represent any vector in mathematical form then we will multiply the magnitude of that vector with unit vector of the direction.

if a = magnitude of vector

and = unit vector

then = a

**Important Points :**

**(i)**If we multiply a vector with negative sign, then the magnitude will not change only direction will change

**(ii)**Two vectors are called equal if their magnitudes and direction are same. So we can transfer any vector (to any where) parallel to itself.

**(iii)**If two vectors has same direction then the unit vector of both of them will be similar. Because magnitude of unit vector is unity.

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