Here you will learn types of vectors in maths.
Let’s begin –
Types of Vectors in Maths
(a) Zero or Null Vector
A vector whose initial and terminal points are coincident is called the zero or the null vector.
Thus, the modulus of the null vector is zero but it can be thought of as having any line as its line of support. The null vector is denoted by \(\vec{0}\).
Vectors other than the null vector are called zero vectors.
(b) Unit Vector
A vector whose modulus is unity, is called a unit vector. The unit vector in the direction of a vector \(\vec{a}\) is denoted by \(\hat{a}\), read as ‘a cap’.
Thus, | \(\hat{a}\) | = 1
(c) Like and Unlike Vectors
Vectors are said to be like when they have the same sense of direction and unlike when they have opposite directions.
(d) Collinear or Parallel Vectors
Vectors having the same or parallel supports are called collinear vectors.
(e) Co-initial Vectors
Vectors having the same initial point are called co-initial vectors.
(f) Co-planar Vectors
A system of vectors is said to be coplanar, if their supports are parallel to the same plane.
Note that the two vectors are always coplanar.
(g) Coterminous Vectors
Vectors having the same terminal point are called coterminous vectors.
(h) Negative of a Vector
The vector which has the same magnitude as the vector \(\vec{a}\) but opposite direction, is called the negative of \(\vec{a}\).
(i) Reciprocal of a Vector
A vector having the same direction as that of a given vector \(\vec{a}\) but magnitude equal to the reciprocal of the given vector is known as the reciprocal of vector a.
(j) Localized and Free Vectors
A vector which is drawn parallel to a given vector through a specified point in space is called a Localized Vector.
If the value of a vector depends only on the length and direction and is independent of its position in the space, it is called a free vector.
