A vector is a line segment oriented by an arrowhead drawn at one of its ends:
Point A is called origin and the point of the arrow (B) is called extreme vector.
All vectors consist of the following elements:
- Magnitude or modulus: is the length or size of the segment.
- Direction: is the direction of the line that contains the vector or any line parallel to it.
- Direction: indicated by the arrowhead (end), it indicates to which side of the line of action the vector is directed.
They are those whose module is zero (0) and cannot be assigned an address or meaning. The end and origin of these vectors lie at the same point.
Example: Sean A y B two vectors that have the same module and the same direction, but different sense. When making a sum of both vectors, we obtain a null vector.
We know that:
B = – A
A + B = A + (-A) = A - A = 0
They are those vectors that have unit (1) as a module. They are generally denoted with a circumflex accent (commonly called a “little hat”), “^”.
Example: Vectors associated with the directions of the Cartesian coordinate axes x, y, z, are generally designated by the unit vectors î, ĵ, k.
Team or equal vectors
Another vector that has the same modulus and the same direction and sense is called an equipment vector of a given one.
Another vector that has the same modulus and the same direction, but opposite sense is called the opposite vector of a given one.
The opposite is
The opposite vector is - A = (-Ax, -TOy), that is to say:
A = – A
Concurrent or Angular Vectors
They are those vectors whose directions or lines of action pass through the same point. They are also called angular because they form an angle between them.
A, B y C are concurrent
They are those vectors that share the same line of action, that is, if they are parallel to a line or are on the same line.
Two vectors A = (Ax, TOy, TOz) Y B = (Bx, By, Bz) are collinear if:
- The relationships of its coordinates are the same.
( TOx / Bx ) = (Ay / By ) = (Az / Bz )
- The vector product of both vectors is null (zero), that is:
A × B = (AyBz - TOzBy) î + (AxBz - TOzBx) ĵ + (AxBy – AyBx) k = 0
A × B = |A| |B| sinθ = 0
Since θ = 0 or θ = 180 ⁰ (remember that θ is the angle between both vectors).
They are those vectors whose lines of action are located in the same plane, that is, if they are parallel to the same plane or are in the same plane.
A, B y C are coplanar vectors