What are the difference between scalars and vectors?

a scalar just has magnitude (like speed in meters/second)

a vector has speed AND direction (like velocity NW)
You can do scalar speed in your car with a speedometer.
BUT
to get velocity vector
you ALSO need a COMPASS .

Scalars and vectors are both quantities used in mathematics and physics, but they have distinct characteristics.

1. Definition:
- Scalars are quantities that have only magnitude (size) and are described by a single numerical value. Examples include mass, temperature, time, and distance.
- Vectors are quantities that have both magnitude and direction. They are represented by arrows, with the magnitude of the vector indicated by the length of the arrow, and the direction indicated by the direction of the arrow.

2. Representation:
- Scalars can be represented by ordinary numbers, without any special notation or symbols.
- Vectors are typically represented by bold letters (e.g., 𝐯) or with an arrow above the letter (e.g., →v).

3. Operations:
- Scalars obey the usual algebraic operations such as addition, subtraction, multiplication, and division.
- Vectors have their own set of operations, including addition, subtraction, scalar multiplication, dot product, and cross product.

4. Physical meaning:
- Scalars represent physical quantities that only have magnitude, such as mass or temperature.
- Vectors represent physical quantities that have both magnitude and direction, such as velocity or force.

To identify whether a quantity is a scalar or a vector, you need to look for the presence of direction. If direction is relevant, it is a vector, otherwise, it is a scalar. For example, a distance of 5 meters is a scalar because it only indicates the magnitude (5) without any specified direction. On the other hand, the displacement of 5 meters north is a vector because it has both magnitude (5) and direction (north).

To summarize, scalars are quantities that have only magnitude, while vectors have both magnitude and direction.