# What are vectors?

Vectors are **segments of a straight line in a two-dimensional or three-dimensional plane**, also known as a vector space. Their mathematical expression **is represented by a letter with an arrow over it**; at the graphic level,** **it is also represented by an arrow.

Vectors can represent **physical quantities with a magnitude** **and direction,** such as **force, displacement, and speed.** In addition, they are usually represented in planes with coordinates.

**What are the characteristics of vectors?**

In general, vectors have the following characteristics:

**Direction:**represented by the tip of the arrow shown graphically, indicating the place toward which the vector points.**Line:**the vector’s location, which is continuous and infinite in space.**Magnitude:**the length between the start and end of the vector, or where the arrow starts and ends.**Amplitude:**the numerical expression of the graphic length of the vector.**Initial point:**the geometric place where the vector starts graphically.**Name:**the letter that accompanies the vector represented graphically, coinciding with the magnitude or the sum of the initial point and its end value.

**What kind of vectors are there?**

Vectors can be classified as:

**Unit vectors:**their length is one unit, that is, their magnitude is equal to one.**Free vectors:**these have the same direction, line, and magnitude, so their initial point is free or undefined.**Sliding vectors:**their initial point can be slid on a straight line without being considered different vectors.**Fixed vectors:**applied to a certain point.-
**Concurrent or angular vectors:**their lines of action pass through the same point, forming an angle between them. -
**Parallel vectors:**the lines of the vector are parallel. -
**Opposite vectors:**while they have the same line and magnitude, they have opposite directions. **Collinear vectors:**they share the same line of action.**Coplanar vectors:**vectors whose lines of action are located in the same plane.**Axial vectors (also known as pseudovectors):**vectors whose direction indicates an axis of rotation; that is, they are linked to a rotational effect.

**What is the difference between vector and scalar magnitudes?**

In physics, there are two types of magnitudes: **scalar and vector.** The former is **given with a number and units,** while the latter, in addition to being represented by a numerical value, **is identified with a direction and line.**

Choosing scalars or vectors to determine the physical magnitude** will depend on the nature of what is being measured or calculated.** For example, to describe temperatures, densities, or masses, numerical representation is used, and these are understood as scalar magnitudes. However, **to calculate velocities, forces, acceleration, thermal energy, weights, or powers, vectors are used.**

**How are vectors represented graphically?**

When graphed, a vector must meet a set of characteristics, such as:

**Every vector uses an arrow symbol as a graphic representation.**- If the ends of the arrow remain in the same place and order,
**the symbol used to represent it does not change,**regardless of whether it is straight or has a curvature. - Vector
**are usually chained together to indicate their sum,**so the end arrow of the first vector is joined to the initial point of the next one. This way,**the line of the two ends is maintained.** **If a vector arrow closes on itself,**it means that**it does not produce****algebraic operations****.**