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.