TYPES OF VECTORS AND COMPONENTS

TYPES OF VECTORS AND COMPONENTS
TYPES OF VECTORS
a) Polar Vectors: The vector whose direction does not change even though the coordinate system in which it is defined changes is called polar vector or Real vector
Eg: Force, momentum, Acceleration.
b) Axial Vectors: The vectors whose direction changes with the coordinate system in which it is defined changes is called axial vector or Pseudo vector
Eg: Angular velocity, torque, angular momentum
c)Like vectors (or) parallel vectors: Two or more vectors (representing same physical quantity) are called like vectors if they are parallel to each other, however their magnitudes may be different. A

d) Unlike vectors (or) anti parallel vectors: Two vectors (representing same physical quantity) are called unlike vectors if they act in opposite direction however their magnitudes can be different.
            
e) Negative Vector : A vector having the same magnitude and opposite in direction to that of a given vector is called negative vector of the given vector.
                
f)Co-initial vectors: The vectors having same initial point are called co-initial vectors.
            
g)Colinear vectors: Two or more vectors are said to be collinear when they act along the same line however their magnitudes may be different.
Eg: Two vectors as shown are collinear vectors.
                
h) Coplanar vectors: A number of vectors are said to be coplanar if they are in the same plane or parallel to the same plane. However their magnitudes may be different.
     
i)Unit vector : A vector whose magnitude equals one and used to specify a convenient direction is called a unit vector.
    A unit vector has no units and dimensions. Its purpose is to specify the direction of given vector.
In Cartesian coordinate system, unit vectors along positive x, y and z axis are symbolized as  \(\widehat i,\widehat y , \widehat k\) respectively. These three unit vectors are mutually perpendicular and their magnitudes
      \(|\widehat i| = |\widehat y| = |\widehat k|\)  =1
If   \(\overrightarrow A \)is a non zero vector, then the unit vector in the direction of \(\overrightarrow A \) is given by
\(\widehat A = \frac{{\overrightarrow A }}{{|\overrightarrow A |}}\)
j) NULL VECTOR (OR) ZERO VECTOR 
A vector whose magnitude is equal to zero is called a null vector. Its origin coincides with terminus and its direction is indeterminate.
Examples of zero vector:
1.The velocity of a particle at rest.
2.The acceleration of a particle moving at uniform velocity.
3.The displacement of a stationary object over any arbitrary interval of time.
4.The position vector of a particle at the origin 
5.At the highest point of a vertically projected body. its velocity vector is null vector.
Note : \(\overrightarrow A + \overrightarrow 0 = \overrightarrow A \)
Note :In our study, vectors do not have fixed locations. So displacing a vector parallel to itself leaves the vector unchanged. Such vectors are called free vectors. However, in some physical applications, location or line of application of a vector is important. Such vectors are called localized vectors.