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Types of Vectors

Learn about the different types of vectors in this page. First get introduced with the concept of vector. Physical quantities are divided into two categories – scalar quantities and vector quantities.

Scalar : A quantity having only magnitude is called a scalar. It is not related to any fixed direction in space. Examples: mass, volume, density, work, temperature, distance, area, real numbers etc. To represent a scalar quantity, we assign a real number to it, which gives its magnitude in terms of a certain basic unit of a quantity. 

Vector : A quantity having both magnitude and direction is called a vector. Examples: displacement, velocity, acceleration, momentum, force, moment of a force, weight etc.


Representation of vectors


Vectors are represented by directed line segments such that the length of the line segment is the magnitude of the vector and the direction of arrow marked at one end denotes the direction of the vector.

                                                                            vectorsA vector denoted by `veca` `vec(AB)` is determined by two points A, B such that the magnitude of the vector is the length of the line segment AB and its direction is that from A to B. The point A is called initial point of the vector `vec(AB)` and B is called the terminal point. Vectors are generally denoted by `veca` , `vecb` , `vecc` … (read as vector a, vector b, vector c, … )


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Types of Vectors - Explained


The Differnt types of vectors are explained below:

Zero or Null Vector: A vector whose initial and terminal points are coincident is called a zero or null or a void vector. The zero vector is denoted by `veco`. Vectors other than the null vector are called proper vectors.

Unit vector: A type of  vector whose modulus is unity, is called a unit vector. The unit vector in the direction of `veca` is denoted by `hata``hata` | = 1. The unit vectors parallel to  `veca` are ±`hata` (read as ‘a cap’). Thus |

Like and unlike vectors: Vectors are said to be like type of vectors when they have the same sense of direction and unlike when they have opposite directions.

Co-initial vectors: Vectors which have the same initial point are called co-initial vectors.

Co-terminus vectors: Vectors having the same terminal point are called co-terminus vectors.

Collinear or Parallel vectors: Vectors are said to be collinear or parallel if they have the same line of action or have the lines of action parallel to one another.

Coplanar vectors: Vectors are said to be coplanar if they are parallel to the same plane or they lie in the same plane.

Negative vector: The vector which has the same magnitude as that of `veca` but opposite direction is called the negative of `veca` and is denoted by − `veca` . Thus if AB=" `veca` then BA="− `veca` .


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