From you responses in Activity 1, observe that, quantities that are described by only their magnitude are called scalar quantities that are completely determined by the magnitude only and vector quantities are quantities that are determined using both magnitude and direction.

Definition

1. A quantity which can be completely described by its magnitude expressed in some particular unit is called a scalar quantity.
2. A quantity which can be completely described by stating both its magnitude expressed in some particular unit and its direction is called a vector quantity.

A vector is represented by an arrow with initial point and terminal point, the overhead arrow indicates the direction and the magnitude of the vector is the distance between the initial and terminal points of the arrow representing the vector.

The following procedure can be used to convert directed line segments to coordinate form and vice versa.

1. If P(x₁, y₁) and Q(x₂, y₂) are two points on the plane, then the coordinate form of the vector v represented by
   
   is v = (x₂ – x₁, y₂ – y₁). Moreover, the magnitude of v, denoted by |v|, is defined by:
   
2. If v = (x, y), then v can be represented by the directed line segment in standard position, from O (0, 0) to Q(x, y).