IIT (NTSE/Olympiad)  

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 ax is a component of any vector in x-direction, ay is a component in y-direction and azis component in z-direction then

where ax, ay, az 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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