Scalar:
A scalar is a physical quantity that has only magnitude and no direction. It is described by a single value and can be positive, negative, or zero. Scalars are completely defined by their magnitude and unit. Examples of scalars include time, mass, temperature, and speed.

Vector:
A vector is a physical quantity that has both magnitude and direction. It is represented by an arrow in a specific direction and its length represents the magnitude. Vectors are defined by their magnitude, direction, and unit. Examples of vectors include displacement, velocity, acceleration, and force.

Differences between Scalar and Vector:

1. Representation:
- Scalars are represented by a single value.
- Vectors are represented by an arrow or a line segment with a direction and magnitude.

2. Magnitude:
- Scalars only have magnitude and no direction.
- Vectors have both magnitude and direction.

3. Examples:
- Scalars: Time (e.g., 5 seconds), mass (e.g., 2 kilograms), temperature (e.g., 30 degrees Celsius).
- Vectors: Displacement (e.g., 10 meters east), velocity (e.g., 20 meters per second north), force (e.g., 30 newtons upwards).

4. Operations:
- Scalars can be added, subtracted, multiplied, and divided using basic arithmetic operations.
- Vectors can also be added, subtracted, multiplied, and divided, but these operations have specific rules based on their direction and magnitude.

5. Components:
- Scalars have only one component, which is their magnitude.
- Vectors have two components: magnitude and direction.

6. Physical Quantities:
- Many physical quantities can be represented as scalars, such as time, mass, and temperature.
- Physical quantities that involve both magnitude and direction, such as displacement, velocity, and force, are represented as vectors.

7. Notation:
- Scalars are typically represented by lowercase letters (e.g., t for time, m for mass, T for temperature).
- Vectors are often represented by boldface lowercase letters (e.g., d for displacement, v for velocity, F for force) or by adding an arrow symbol above the letter (e.g., ⟶d, ⟶v, ⟶F).

In summary, scalars only have magnitude, while vectors have both magnitude and direction. Scalars are represented by a single value, while vectors are represented by an arrow or line segment. Scalars can be added, subtracted, multiplied, and divided using basic arithmetic operations, while vectors have specific rules for vector operations.