Vector - Types of Vector, Definition, Practice Problems, FAQs

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

• What is a Vector?
• Unit Vector
• Position Vector
• Axial Vector
• Practice Problems of Vector
• FAQs of Vector

What is Vector?

The physical quantities that have magnitude and direction for definition are called vectors.

Types of Vector

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

Zero Vector

• If the starting and finishing point of a vector coincide with each other, then it is known as a zero vector or null vector.
• The magnitude of zero vectors is zero, and does not have any direction.
• On a cartesian coordinate system, zero vector is represented by a point.

Unit Vector

• Vectors having magnitude equal to 1 are known as a unit vector.
• If is a vector having a magnitude then the unit vector is denoted by  in the direction of the vector and has the magnitude equal to 1.

• In general, unit vector along x -  axis, y -  axis and z -  axis are respectively.

Position Vector

• Position vector is a vector which tells about the position of a point in space with respect to a reference point.
• If O is taken as reference origin and P  is an arbitrary point (x.y.z) in space, then will be the position vector of the point p.

Co-Initial Vectors

• Vectors which have the same initial point are referred to as co-initial vectors.
• The vectors and are called co-initial vectors as they have the same starting point.

Coplanar Vectors

• Three or more vectors lying on a single plane or parallel to the same plane are known as coplanar vectors.
• Figure shows three vectors lie on x - z plane.

Collinear Vectors

• Vectors which are either along the same line or parallel lines are known as collinear vectors.
• As shown in the left figure, two vectors along the same line and right figure two vectors are along parallel lines. 

Like and Unlike Vectors

• The vectors which have the same direction are known as like vectors.
• Vectors which have the opposite direction with respect to each other are termed to be unlike vectors.

Equal 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).

Negative of a Vector

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.

Displacement 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.

Polar Vectors

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

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.

Practice Problems of Vector

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?

Answer:

After the trip, the person reaches the point (3,3) and whose position vector given by .

FAQs of Vector

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?

Answer: 1.

Related Topics to Vector in Physics

• Scalar and Vector
• Vector Subtraction
• Lami's Theorem
• Vector Addition

NCERT Class 11 Physics Chapters