Vectors are mathematical and physical entities characterized by having both a magnitude (size or length) and a direction. They are often represented graphically as arrows, where the length of the arrow corresponds to the magnitude and the arrowhead indicates the direction

. In geometry and physics, vectors describe quantities that cannot be fully expressed by a single number (a scalar) because they involve direction as well as magnitude. Examples of vector quantities include displacement, velocity, acceleration, and force

. Unlike scalars, which only have magnitude (like speed or mass), vectors provide more complete information about a physical quantity by specifying where and how it acts. Vectors can be added together and multiplied by scalars (numbers), and these operations follow specific algebraic rules. This leads to the concept of vector spaces in mathematics, where vectors are elements that can be manipulated according to these rules

. Key points about vectors:

• They have an initial point (tail) and a terminal point (head).
• Two vectors are equal if they have the same magnitude and direction, regardless of their position

• Types of vectors include zero vectors (magnitude zero), unit vectors (magnitude one), and others depending on their properties and relationships

• Vectors are fundamental in fields like physics, engineering, and computer graphics for representing directional quantities and performing calculations involving them

In summary, vectors are quantities defined by both how much (magnitude) and which way (direction), essential for describing many physical and mathematical phenomena.