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Vectors in Algebra

A vector is a physical quantities that has both magnitude and direction.Vectors are represented by directed line segments like

vector represented by line segment
Length of dircted line segment is called magnitude of vector and direction represented by arrow marks.
vector representation

Types of Vectors

  1. Zero or Null Vector
  2. Unit Vector
  3. Like and Unlike Vector
  4. Collinear or Parallel Vector
  5. Co-initial Vector
  6. Co-Planar Vector
  7. Coterminous Vector
  8. Negative of a Vector
  9. Reciprocal of a Vector
  10. Localized and Free Vectors

Zero or Null Vector :Null or zero vector are vector whose initial and terminal points are coincident means starting or end points are or bull vectors is denoted by 0(zero) like 0
Unit Vector :if modulus of any vectors is unity then that vectors is called unit vectors. unit vectors is denoted by |a|=1
Collinear or Parallel Vector :Vectors having same or parallel supports are known as Collinear or Parallel Vector.

Like and Unlike Vector :Veictors having same sense of direction are known as like vectors and if vectors having opposite sense of direction than that known as unlike vector.

Co-initial Vector :if two or more vectors having same initial point then that vectors known as co-initial vectors.
co-inital vectors example

Co-Planar Vector :

Coterminous vectors : if two or more vectors having same terminal point then that vectors known as Coterminous vectors.
coterminous vectors example
Negative of a Vector : Any vector having the same magnitude as the vector A but oposite direction is known as negative of vector A. we represent negative vector as -a if AB=a then BA=-a if two vector A and B having the same magnitude(vector A magnitude is same as vector B magnitude) and direction is oposite then vector B is negative of vector A.
Reciprocal of A vector : Vector is reciprocal to other vector if and only if vector having same direction but magnitude is equal to the reciprocal of other vector.