Vectors

A vector is an orientated segment. We represent it by AB, where A is the origin and B is the extreme.

The characteristics of a vector are:
- Magnitude or length, |AB|: the length of the segment.
- Direction: the direction of the straight line that contains it and the direction from the origin to the extreme (sense).

The set of vectors with the same magnitude and directions is called free vector. The vector of this set that has the origin in O and the extreme in the point P is called the position vector of P.

The coordinates of a vector are:

We calculate the magnitude of a vector by using the Pythagorean Theorem:

The angle describing the direction of a vector is called its argument:

Example:

Exercise: If u(3,-2), A(1,t), B(-3,3):

a) Calculate the magnitude and argument of u.

b) Calculate t, if AB(-4,-2).

Solutions: a)|u|= √13; θ = 146º18'36''; b) 5