• A quantity which is described by only magnitude is called scalar.
• Quantities that need both magnitude and direction to describe them are called vector quantities (or simply vectors).
• A vector is denoted by a directed arrow. Its length is called the magnitude. The direction it points is called the direction of the vector.
• A vector is represented by an arrow the point O is called the initial point and P is called the terminal point. Sometimes, vectors are represented by using letters or a letter with a bar over it such as etc.
• The magnitude of a velocity is the speed; the magnitude of a displacement is distance. Thus, speed and distance are scalar quantities
• A magnitude is always a positive number.
• Vectors can be described geometrically or algebraically: geometrically as a directed arrow and algebraically as a column vector.
• Two vectors are said to be equal if they have the same magnitude and the same direction.
• If two vectors have same or opposite directions then they are parallel. Indeed, two vectors are parallel if one is a scalar multiple of the other.
• For any two vectors

(the Triangle law)

• A vector that has no magnitude and direction is called a zero vector or null vector.
• The diagonal of a parallelogram is the sum of the side vectors. This is called the Parallelogram Law.
• Subtraction of vectors

is the same as

• Multiplying a vector by a scalar k either enlarges or shortens the vector. If  it enlarges the vector and if  it shortens the vector. If k > 0,  the direction of the vector is unchanged; multiplying a vector by k< 0 changes the direction of the vector into the opposite direction.
• If the initial and terminal points of a vector are (x₁, y₁) and (x₂, y₂) then its position vector can be calculated as P = (x₂ −x₁, y₂ −y₁) and is denoted by

• Any vector

and