A vector has direction and magnitude both but scalar has only magnitude.
Two vectors a and b are said to be equal written as a = b, if they have (i) same length (ii) the same or parallel support and (iii) the same sense.
A vector whose initial and terminal points are coincident is called zero or null vector. It is denoted by 0.
A vector whose magnitude is unity is called a unit vector which is denoted by n^{ˆ}
^{}
A vector having the same magnitude as that of a given vector a and the direction opposite to that of a is called the negative of a and it is denoted by —a.
Vectors are said to be like when they have the same direction and unlike when they have opposite direction.
Vectors having the same or parallel supports are called collinear vectors.
Vectors having same initial point are called coinitial vectors.
A vector which is drawn parallel to a given vector through a specified point in space is called localized vector.
A system of vectors is said to be coplanar, if their supports are parallel to the same plane. Otherwise they are called noncoplanar vectors.
Example: In the figure given below, identify Collinear, Equal and Coinitial vectors:
Solution: By definition, we know that
Example: In the given figure, identify the following vectors
Solution:
209 videos443 docs143 tests

1. What are the different types of vectors based on direction? 
2. How are unit vectors defined in the context of vectors? 
3. Can you provide examples of parallel vectors in realworld scenarios? 
4. What is the significance of position vectors in vector analysis? 
5. How are zero vectors defined and what role do they play in vector algebra? 
209 videos443 docs143 tests


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