In physics, Vectors quantities are that quantities have a magnitude and a direction. If we take force as an example, we can show it in terms of the magnitude of the force and the direction of the force. Such quantities in physics are called vector quantities. When we take temperature as an example, we can understand its magnitude ( for example 100°C) but we can’t say its direction. Such types of quantities are called scalar quantities. In this article, we look at the definition and types of vectors.
Definition of vectors
Vector is a type of quantity that has both magnitude and direction. It helps in the study of motion. Vector quantities are represented by an arrow in which the direction is the same as that of the quantity and the length is proportional to the quantity’s magnitude.
Examples of vectors in physics
- Force
- Acceleration
- Momentum
- Velocity
- Torque
- Acceleration
- Angular velocity
- Electric field
Characteristics of a vector quantity
- Two vectors are said to be equal if they have the same magnitude and the same direction. For example, consider two forces with an equal magnitude of 5 N, if they are acting in a different direction then they are not equal.
- The negative vector is a vector that has an opposite direction to the reference direction.
- The sum of any two vectors – A, B can be visualized by placing the tail of vector B at the head of vector A and drawing vector C which starts from the tail of A and ending at the head of B so that it completes the triangle.
- They also have associative and distributive property
Types of Vectors
- Unit vector
- Zero vector
- Position Vector
- Co-initial vector
- Coplanar vector
- Like and unlike vector
- Collinear vector
- Equal vectors
- Displacement vector
Unit Vector
As the name suggests this vector has a unit magnitude in a specific direction.
Zero Vector
A vector having a zero magnitude is called a zero vector. It is denoted by a zero bar.
Position vector
This vector helps in describing the position of a moving object with respect to a fixed object(or reference). Its one end is fixed and the other end is attached to the moving point. It will change the length or direction or both at the same time.
Co-Initial Vectors
If the given two vectors are co-initial only if they start from the same initial point.
The diagram shown below is an example of a co- initial vector.
Co-Planar Vectors
They are the vectors that lie on the same plane in a three-dimensional space. They are always parallel to the same plane.
Like and unlike Vectors
Two vectors are said to be like vectors if their direction will be the same, whereas, in unlike vectors, the direction will be opposite to each other. The given diagram shows the difference between like and unlike vectors.
Here we can see in the above image that both the vectors A and B are in the same direction through their magnitude may or not be equal but they are called like vectors.
Collinear Vectors
Collinear vectors are any two or more vectors that are parallel to the same line irrespective of their magnitude and direction.
Equal Vectors
They are any two vectors having the same magnitude and direction. They may or may not be having the same initial point.
Displacement Vectors
It is the vector distance between the initial and final point of the destination. The change in the position vector of an object is also known as the displacement vector.
Can two vectors be multiplied?
Vectors can be multiplied, but since the direction is involved, the multiplication is not straightforward. There are mainly 2 methods used:
- Dot product: This multiplication gives a scalar quantity as output.
- Cross product: This multiplication yields a vector in the perpendicular direction to the plane containing the vectors.
