A vector has direction and magnitude both but scalar has only magnitude.
Magnitude of a vector a is denoted by |a| or a. It is non-negative scalar.
Equality of Vectors
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.
Types of Vectors
(i) Zero or Null Vector A vector whose initial and terminal points are coincident is called zero or null vector. It is denoted by 0.
(ii) Unit Vector A vector whose magnitude is unity is called a unit vector which is denoted by nˆ
(iii) Free Vectors If the initial point of a vector is not specified, then it is said to be a free vector.
(iv) Negative of a Vector 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.
(v) Like and Unlike Vectors Vectors are said to be like when they have the same direction and unlike when they have opposite direction.
(vi) Collinear or Parallel Vectors Vectors having the same or parallel supports are called collinear vectors.
(vii) Coinitial Vectors Vectors having same initial point are called coinitial vectors.
(viii) Coterminous Vectors Vectors having the same terminal point are called coterminous vectors.
(ix) Localized Vectors A vector which is drawn parallel to a given vector through a specified point in space is called localized vector.
(x) Coplanar Vectors A system of vectors is said to be coplanar, if their supports are parallel to the same plane. Otherwise they are called non-coplanar vectors.
(xi) Reciprocal of a Vector A vector having the same direction as that of a given vector but magnitude equal to the reciprocal of the given vector is known as the reciprocal of a.
i.e., if |a| = a, then |a-1| = 1 / a.
Solution: By definition, we know that
More Solved Examples
Question: In the given figure, identify the following vectors
|1. What are the different types of vectors?|
|2. How are position vectors different from displacement vectors?|
|3. What do velocity vectors represent?|
|4. How are force vectors different from acceleration vectors?|
|5. Can vectors have negative magnitudes?|