Vectors are classified into various categories depending on their operation and application. A vector that tells the position of an object is called position vector and a vector that gives you displacement of a particle is displacement vector , so vectors can be of various types.
Table of Contents
The physical quantities that have magnitude and direction for definition are called vectors.
Vector may have the following types-
1. Zero Vector
2. Unit Vector
3. Position vector
4. Co-Initial Vectors
5. Coplanar Vectors
6. Collinear Vectors
7. Like and Unlike Vectors
8. Equal Vectors
9. Negative of a Vector
10. Displacement vector
11. Axial Vectors
12. Polar Vectors
Two or more vectors are said to be equal when their magnitude is equal and also their direction is the same (As shown in figure).
Vector having the same magnitude and opposite in the direction of a given vector is said to be negative of a vector.
Suppose PQ is the given vector then QP will be negative of the given vector.
If a point is displaced from position A to B then the displacement AB represents a vector which is known as the displacement vector.
Vectors that have some initial point or a point of application are called polar vectors.
The direction of the polar vector remains unchanged irrespective of the coordinate system chosen.
Displacement, force, etc are polar vectors.
Axial vectors describe rotational motion, and act along the axis of rotation (according to the right hand screw rule which will be discussed in upcoming chapters).
For example angular velocity and angular acceleration are axial vectors.
Question 1. Find the unit vector of .
Answer: Finding the magnitude of vector
Question 2. Find the position vector of point (2,3, -5) in space.
Answer: Position vector of point (X,Y,Z) is
Similarly, for point .
Question 3. A particle which is initially at point (6, -3,2) is moved to another point (1,7,5) find the displacement of particle.
Question 4. A Woman initially at origin starts to walk 3 m towards north, then 6 m towards east, then 5 m towards the west.position vector of woman at the end of the trip?
After the trip, the person reaches the point (3,3) and whose position vector given by .
Question 1. What are the types of vector?
Answer: zero vector, unit vector, position vector, coinitial vector, coplanar vector, collinear vector, like and unlike vector, equal vector, negative of a vector, displacement vector, polar vector, axial vector.
Question 2. What do you mean by Position vector ?
Answer: A position vector is defined as a vector that indicates either the position or the location of any given point with respect to any arbitrary reference point.
Question 3. What do you mean by Displacement vector ?
Answer: Displacement vector can be simply defined as the change in position vector of a particle.
Question 4. What is the magnitude of a Unit vector?
|Physical World||Units and Measurements|
|Motion in a Plane||Laws of Motion||Work Energy and Power|
|Gravitation||Mechanical Properties of Solids|
|Mechanical Properties in Liquids||Thermal Properties of Matter||Thermodynamics|