Adding two or more vectors is called vector addition. What is a vector? Any quantity which has magnitude along with direction is a vector. Some examples of vector quantities are displacement, velocity, acceleration, force, pressure, etc. Mathematical operations can be performed between two or more vectors. In this article, we will learn about the vector addition of two quantities using analytical methods.
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What is Vector Addition?
The process of adding two or more vectors is called vector addition. Depending on the direction of the vector, vector addition is categorised into two types. They are –
- Parallelogram law of vector addition
- Triangular law of vector addition
Consider a vector A and vector B
The method of vector addition is chosen based on the arrangement of the head and tail of vectors.
- If two vectors are arranged head to tail the triangular law of vector addition is followed.
- If two vectors are arranged head to head or tail to tail then, the parallelogram law of vector addition is followed.
Parallelogram Law of Vector Addition
If two vectors are arranged head to head or tail to tail then, the parallelogram law of vector addition is carried out.
Statement
“If two vectors are considered to be the adjacent sides of a parallelogram, then the resultant of two vectors is given by the vector that is a diagonal passing through the point of contact of two vectors.”
Method
Step-wise vector addition of two vectors using parallelogram law of vector addition is given below-
Step 1:
Consider two vectors; vector A and vector B
Step 2:
Bring the tail of vector A to the tail of vector B. Here the direction of vectors is not changed.
Step 3:
Draw two lines parallel to vector A and vector B with the same magnitude, in a way to complete a parallelogram.
Step 4:
Join the point o and r by a straight line with an arrow pointing towards the r. This is the diagonal of the parallelogram.
And this is the resultant vector vector R
Triangular Law of Vector Addition
If two vectors are arranged head to tail the triangular law of vector addition is carried out.
Statement
“When two vectors are represented by two sides of a triangle in magnitude and direction were taken in the same order then the third side of that triangle represents in magnitude and direction the resultant of the vectors.”
Method
Step-wise vector addition of two vectors using the triangular law of vector addition is given below-
Step 1:
Consider two vectors, vector A and vector B
Step 2:
Bring the head of vector A to the tail of vector A. Here the direction of vectors is not changed.
Step 3:
Join the tail of vector A to the head of vector B by a straight line with an arrow pointing towards the head of vector B
This new vector is the resultant vector vector C
Why Vector Addition is Important?
In physics, vector quantities like force interact with each other and produce a resultant effect on the objects upon which they are applied. Since the impact of all these forces is taken into consideration when finding the nature of the motion of the system, so, in order to find the resultant of these forces, operations such as addition, subtraction and multiplication are required to be performed on these forces.
Frequently Asked Questions – FAQs
What is vector addition?
Why vector addition is important in physics?
What is a vector?
Name some vector quantities in physics.
Name two types of vector addition.
When do we use the triangular law of vector addition?
When do we use the parallelogram law of vector addition?
State parallelogram law of vector addition.
State triangular law of vector addition.
In parallelogram law of vector addition, what represents the resultant vector?
Hope you have learned about vector addition by parallelogram law of vector addition and triangular law of vector addition along with the statement, step-by-step method.
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| Constants In Physics |
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