Vectors and scalars are fundamental concepts in physics, and they differ primarily in their characteristics: vectors possess both magnitude and direction, while scalars have only magnitude.

In the realm of physics, quantities are typically classified into two categories: scalars and vectors. Scalars are defined by their magnitude alone, which is a numerical value. Common examples of scalar quantities include time, temperature, volume, speed, mass, and energy. These quantities are characterized solely by their numerical value, without any associated direction.

In contrast, vectors are quantities that are defined by both a magnitude and a direction. Examples of vector quantities include displacement, velocity, acceleration, and force. The inclusion of direction is what distinguishes a vector from a scalar. For instance, stating that a car is moving at a speed of $60 \, \text{km/h}$ describes a scalar quantity (speed). However, if we specify that the car is moving at $60 \, \text{km/h}$ toward the north, this describes a vector quantity (velocity) because it incorporates a directional component.

Graphically, the direction of a vector is often represented by an arrow. The length of the arrow corresponds to the magnitude of the vector, while the orientation of the arrow indicates its direction. This visual representation is particularly useful for understanding and manipulating vectors.

Mathematically, vectors can be expressed as ordered pairs or triples, depending on whether they exist in two or three dimensions. For instance, a vector in two dimensions can be represented as $(x, y)$, where $x$ denotes the magnitude in the x-direction and $y$ denotes the magnitude in the y-direction. This mathematical framework allows for operations such as addition, subtraction, and multiplication of vectors, which are essential for solving various physics problems.

In summary, the fundamental distinction between vectors and scalars lies in the presence of direction. Scalars are straightforward numerical values, while vectors are quantities that include both magnitude and direction. Grasping this distinction is crucial for the study of physics, as numerous physical quantities are vectors.