Addition and Subtraction of Vectors

Vector Addition

1. When and , the vector sum is:
   
   
2. In the parallelogram , if and , the vector sum is:
   
   

Properties of Vector Addition

For any three vectors , , and :

1. Commutative Property:
2. Associative Property:

For any vector :

1. Adding the zero vector does not change the vector
   
2. Adding a vector and its negative results in the zero vector
   

Additionally, the sum of a vector and its reverse is the zero vector

Vector Subtraction

When and , the difference of the vectors is: