Meaning of a Vector

1. Vector
   A physical quantity that has both magnitude and direction is called a vector. A vector in a plane is specifically called a plane vector.
   
   
2. Vector
   A vector is represented by an arrow, which shows both its magnitude and direction. The length of the arrow represents the magnitude of the vector, and the direction of the arrow represents the vector’s direction. A vector that points from point to point and has a magnitude equal to the length of the line segment is denoted as:
   
   
   
   The point is called the initial point of the vector , and point is called the terminal point. When a vector is represented by a single letter, it is denoted as , , , etc.
   
   
3. Unit Vector: A vector with a magnitude of
   The magnitude of a vector is denoted as . A vector with a magnitude of is called a unit vector.
   
   
   
   
   
4. Zero Vector : A vector where the initial and terminal points coincide
   The magnitude of a zero vector is , and it has no defined direction.
   
   
5. Equal Vectors
   In the figure below, vector can be translated to overlap with vector , meaning that while their initial points differ, their magnitudes and directions are identical.
   
   
   
   Vectors and are said to be equal. This is denoted as:
   
   
6. Vectors with Equal Magnitudes but Opposite Directions
   In the figure below, the vectors and have the same magnitude but opposite directions.
   
   
   
   A vector that has the same magnitude as but points in the opposite direction is denoted as: