Vector and scalar quantities: see the differences!

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vector quantities and greatnessesscalars they are types of physical quantities that depend on different information to be defined. For scalar quantities, it is necessary to know their module (or norm) and the unityinmeasure. For vector quantities, it is necessary to know, in addition to the modulus and unit of measure, its direction and sense.

Physics is full of vector and scalar quantities. To know how to identify each of them, it is necessary to understand what defines them, therefore knowing what the characteristics of the greatnessesscalars and vectors, know the difference between greatnessesfundamentals and derivatives and compare direct magnitudes andinverselyproportional. This knowledge permeates all the contents of the Physics, being, therefore, very useful for the study of this area of knowledge.

Read too: What is greatness?

Differences between scalar and vector quantities

All physical quantities can be classified into two types: the greats scalars and the vectors. The most basic difference between these two types of quantities is that scalars can be satisfactorily represented by just the

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number and of a unityinmeasure. In contrast, vector quantities need to be expressed based on more information, such as your valuenumeric, direction and sense, plus a unit of measure.

→ scalar quantities

magnitudesscalars are those that can be written in the form of a number, followed by a unit of measurement. In other words, they are completely defined if we know their value, also called a modulus, and how it is measured.

Examples of scalar quantities are the length, O time, a temperature and the pasta. Check out some ways in which these quantities can be expressed:

1 m - a meter; 10 cm – ten centimeters; 2mm – two millimeters.
10 s – ten seconds; 15 min - fifteen minutes; 1 h - one hour.
25º C – twenty-five degrees Celsius; 86º F – eighty-six degrees Fahrenheit; 10K – ten kelvin.
200 g – two hundred grams; 10 mg – ten milligrams; 2 kg – two kilograms.

In short:

scalar quantities they are completely defined by a number and a unit of measure.

Lookalso:Everything you need to know about physics Mechanics that fall in Enem

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→ vector quantities

vector quantities need to be expressed by a number (module), one direction, a sense is unityinmeasure. This is to say that these quantities can be expressed through a arrow (vector), that is, to define them, it is necessary to take into account the point of view of the observer.

The figure shows that the house position is a vector quantity, as it depends on the views of observers A and B.

Before we continue to discuss what vector quantities are, it is necessary to understand the difference between module, direction and sense:

Module: measure or the size of the vector that represents the vector quantity.
Direction: space dimension that depends on the guidance system that is used. There are directions such as width, height and depth, or even the horizontal and vertical direction, or the x, y and z direction (used in the Cartesian system), or even the east-west, north-south direction.
Sense: the orientation whether it is up or down, right or left, positive or negative, east or west, north or south. Every direction has two directions, which are like the arrowhead of each vector.

Check out some examples of vector quantities:

Position
Displacement
Speed
Strength
Acceleration

In addition to being vector quantities, what is common to all of these quantities listed above? All depend on a direction it is a sense. For example, if someone asks you Where is the bakery, it is not enough to answer that it is 50 m away, it is necessary to establish some systemof reference, like the following:

To reach the bakery, turn right (sense) from here (origin of the reference system) and move straight (direction), running through50 m (module and unit of measure).

In short:

vector quantities they are completely defined by a number, a unit of measure, a direction and a sense.

Read too: Vector operations

physical magnitudes

Since we are dealing with vector and scalar quantities, it is pertinent to understand what a physical quantity is. physical magnitudes they are all the characteristics inherent in a body or in any kind of phenomenon that can be measured. From a basic set of physical greatness, known as fundamental quantities, it is possible to express all other quantities. In addition, to be expressed quantitatively, that is, in numbers, physical quantities must be defined from a measurement system. Currently, the measurement system used by the scientific community and almost all over the world is the International System of Units, also known as SI.

Length is a scalar quantity, and position is a vector quantity, since position, unlike length, depends on the observer.

If you want to understand more deeply about how the magnitudes work, we suggest that you access our text - with a little more advanced content - about the dimensional analysis, That is a tool used for the study of physical quantities.

quantities and measures

At fundamental physical quantities, as well as their measurements, are shown in the table below. In this table you will find these quantities organized according to your Name it's yours symbol, according to the SI. Check out:

Greatness	Symbol and name
Length	m - meter
Time	s - second
Pasta	kg - kilogram
Temperature	K - kelvin
Electric current	A - amp
Quantity of matter	mol - mol
Light intensity	cd - candela

From the quantities shown above, hundreds of others are defined greatnessesderivatives, which are written through the combination of fundamental quantities, such as speed, which is a combination of length and time:

Velocity is a quantity derived from length and time.

Check out some examples of derived quantities and yours units of measure:

Acceleration – [m].[s]^-2
Strength – [kg]. [m].[s]^-2
Density – [kg].[m]^-³
Pressure – [kg]. [m]^-1.[s]^-2

Directly and inversely proportional quantities

When talking about quantities, it is also valid to analyze the issue of proportionality between them. Proportional quantities are those that increase in function of each other. The greater the distance covered by a mobile in a certain time interval, for example, the higher your speed will be, so speed and distance covered are quantities directly proportional. On the other hand, the longer the time needed for this mobile to travel a certain distance, the lower its speed, so we say that speed and time are inversely proportional quantities.

To define whether two quantities are proportional or inversely proportional to each other, we use the symbol α, as shown in the following example: