# 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 vecto**r. 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

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