Components of a Plane Vector

1. Components of a Plane Vector
   Let the position vectors of points and be and , respectively. If the position vector of point is , then: Here, and are called the components of vector . Specifically, is the -component, and is the -component. We can represent vector using its components as:
   
   
   
   
   
2. Magnitude of a Plane Vector and Conditions for Two Vectors to Be Equal
   For vectors and :
1. The magnitude of is:
2. Vectors and are equal if and only if:


3. Operations on Plane Vectors Using Components
   For vectors and :
1. Addition:
   
   
   
   
   
   
2. Subtraction:
   
   
   
   
   
   
3. Scalar Multiplication
   If is a real number:
   


4. Components and Magnitude of a Plane Vector Defined by Two Points
   For two points and :